# wQN P ̌vZ

#### PDPƑ

𓚂\ɂꍇ́Ã{^ĂB

(1) ̎̍ƌW͂ȂłB
(1)$2x-3$
(2)$-4x+\dfrac {1} {2} y$
(3)$a-2b+3cd$
(4)$-5x^2 -y^2 -5$

(1)$2x-3$

F$2x$  ,$-3$
$x$  ̌W$2$

(2)$-4x+\dfrac {1} {2} y$

F$-4x$  ,$\dfrac {1} {2} y$
$x$  ̌W$-4$  ,$y$  ̌W$\dfrac {1} {2}$

(3)$a-2b+3cd$

F$a$  ,$-2b$  ,$3cd$
$a$  ̌W$1$  ,$b$  ̌W$-2$  ,$cd$  ̌W$3$

(4)$-5x^2 -y^2 -5$

F$-5x^2$  ,$-y^2$  ,$-5$
$x^2$  ̌W$-5$  ,$y^2$  ̌W$-1$

(2) ̒P̎͂łB
(1)$3xy$
(2)$-4x^2 y$
(3)$2a^ 2b^3 c$
(4)$9ax$
(5)$\dfrac {2a^2 b} {5}$

(1) Q
(2) R
(3) U
(4) Q
(5) R

(3) ̑̎͂łB
(1)$3x^2 +6$
(2)$a^2 -ab^3$
(3)$3x^2 -6xy+3y^2$
(4)$3-4x^3 +x^5$
(5)$ab^2 c+4a^3 bc^2 -abc$

(1) Q i$3x^2$  ̕ j
(2) S i$-ab^3$  ̕ j
(3) Q i ǂ̍̕$2$  j
(4) T i$x^5$  ̕ j
(5) U i$4a^3 bc^2$  ̕ j

(4) ̎̓ލ܂Ƃ߂܂傤B
(1)$6x+2x$
(2)$4y-2y+y$
(3)$5a-2+a-3$
(4)$-x+2y-3x-4y$
(5)$-a+3b+5a-7b$
(6)$3x^2 +3+4x^2 +6x+2$
(7)$3a^2-6a+5-2a^2 +3a-1$
(8)$3x^3 -6x+4+5x-4x^3$
(9)$-3xy+4y^2 +x^2 -4y^2 -4x^2 +7xy$
(10)$4ab-2bc+ca-6bc+ab-4ca$

(1)$6x+2x$
$=8x$

(2)$4y-2y+y$
$=3y$

(3)$5a-2+a-3$
$=5a+a-2-3$
$=6a-5$

(4)$-x+2y-3x-4y$
$=-x-3x+2y-4y$
$=-4x-2y$

(5)$-a+3b+5a-7b$
$=-a+5a+3b-7b$
$=4a-4b$

(6)$3x^2 +3+4x^2 +6x+2$
$=3x^2 +4x^2 +6x+3+2$
$=7x^2+6x+5$

(7)$3a^2-6a+5-2a^2 +3a-1$
$=3a^2 -2a^2 -6a+3a+5-1$
$=a^2-3a+4$

(8)$3x^3 -6x+4+5x-4x^3$
$=3x^3 -4x^3 -6x+5x+4$
$=-x^3 -x+4$

(9)$-3xy+4y^2 +x^2 -4y^2 -4x^2 +7xy$
$=x^2 -4x^2 -3xy+7xy+4y^2-4y^2$
$=-3x^2 +4xy$

(10)$4ab-2bc+ca-6bc+ab-4ca$
$=4ab+ab-2bc-6bc+ca-4ca$
$=5ab-8bc-3ca$

(5) ̌vZ܂傤B
(1)$\left( 4a-b \right)+\left( 3a+2b \right)$

(2)$2a+\left( -3a-5b \right)$

(3)$\left( 6x+5y \right)-\left( 2x-2y \right)$

(4)$\left( 4x+y \right)-\left( -3y+5x \right)$

(5)$\left( -2a+6b \right)-\left( -2a+5b \right)$

(6)$2x-8y^2 +3x+3y$

(7)$7x^2 -5x+2x^2 -3x$

(8)$\left( 6x^2 -xy-3y^2 \right)-\left( 5x^2 +5xy-y^2 \right)$

(9)$\left( 4ab-bc+5ca \right)-\left( 8ab-bc-5ca \right)$

(10)$\left( -3x^2 -2x-1 \right)+\left( 2x^2 +4x-5 \right)$

(1)$\left( 4a-b \right)+\left( 3a+2b \right)$
$=4a-b+3a+2b$
$=4a+3a-b+2b$
$=7a+b$

(2)$2a+\left( -3a-5b \right)$
$=2a-3a-5b$
$=-a-5b$

(3)$\left( 6x+5y \right)-\left( 2x-2y \right)$
$=6x+5y-2x+2y$
$=6x-2x+5y+2y$
$=4x+7y$

(4)$\left( 4x+y \right)-\left( -3y+5x \right)$
$=4x+y+3y-5x$
$=4x-5x+y+3y$
$=-x+4y$

(5)$\left( -2a+6b \right)-\left( -2a+5b \right)$
$=-2a+6b+2a-5b$
$=-2a+2a+6b-5b$
$=b$

(6)$2x-8y^2 +3x+3y$
$=2x+3x-8y^2 +3y$
$=5x-8y^2 +3y$

(7)$7x^2 -5x+2x^2 -3x$
$=7x^2 +2x^2 -5x-3x$
$=9x^2 -8x$

(8)$\left( 6x^2 -xy-3y^2 \right)-\left( 5x^2 +5xy-y^2 \right)$
$=6x^2 -xy-3y^2 -5x^2 -5xy+y^2$
$=6x^2 -5x^2 -xy-5xy-3y^2 +y^2$
$=x^2-6xy-2y^2$

(9)$\left( 4ab-bc+5ca \right)-\left( 8ab-bc-5ca \right)$
$=4ab-bc+5ca-8ab+bc+5ca$
$=4ab-8ab-bc+bc+5ca+5ca$
$=-4ab+10ca$

(10)$\left( -3x^2 -2x-1 \right)+\left( 2x^2 +4x-5 \right)$
$=-3x^2 -2x-1+2x^2 +4x-5$
$=-3x^2 +2x^2 -2x+4x-1-5$
$=-x^2 +2x-6$

(6) ̌vZ܂傤B
(1)$3a\times 4$

(2)$8x\times \left( -3 \right)$

(3)$-9x\times \dfrac {4} {3}$

(4)$3\left( 4a-2 \right)$

(5)$5\left( -x+3y-1 \right)$

(6)$4\left( a+2b \right)+3\left( 2a-3b \right)$

(7)$2\left( 3x-4y \right)-5\left( x-3y \right)$

(8)$-8\left( x-1 \right)+2\left( 5x+7 \right)$

(9)$4\left( x^2 -4x+2 \right)+3\left( -4x^2 +6x-5 \right)$

(10)$3\left( 2a^2 -ab+b^2 \right)-4\left( 3a^2 -2ab \right)$

(1)$3a\times 4$
$=12a$

(2)$8x\times \left( -3 \right)$
$=-24x$

(3)$-9x\times \dfrac {4} {3}$
$=-12x$

(4)$3\left( 4a-2 \right)$
$=12a-6$

(5)$5\left( -x+3y-1 \right)$
$=-5x+15y-1$

(6)$4\left( a+2b \right)+3\left( 2a-3b \right)$
$=4a+8b+6a-9b$
$=4a+6a+8b-9b$
$=10a-b$

(7)$2\left( 3x-4y \right)-5\left( x-3y \right)$
$=6x-8y-5x+15y$
$=6x-5x-8y+15y$
$=x+7y$

(8)$-8\left( x-1 \right)+2\left( 5x+7 \right)$
$=-8x+8+10x+14$
$=-8x+10x+8+14$
$=2x+22$

(9)$4\left( x^2 -4x+2 \right)+3\left( -4x^2 +6x-5 \right)$
$=4x^2 -16x+8-12x^2 +18x-15$
$=4x^2 -12x^2 -16x+18x+8-15$
$=-8x^2 +2x-7$

(10)$3\left( 2a^2 -ab+b^2 \right)-4\left( 3a^2 -2ab \right)$
$=6a^2 -3ab+3b^2 -12a^2 +8ab$
$=6a^2 -12a^2 -3ab+8ab+3b^2$
$=-6a^2+5ab+3b^2$

(7) ̌vZ܂傤B
(1)$12a\div 2$

(2)$30x\div \left( -5 \right)$

(3)$-24x\div 6$

(4)$12x\div \dfrac {1} {3}$

(5)$20a\div \dfrac {4} {5}$

(6)$\left( 6a+8 \right)\div 2$

(7)$\left( 9x-12y+6 \right)\div \left( -3 \right)$

(8)$\left( 4x-8y \right) \div \dfrac {1} {2}$

(9)$\left( 8x+4y \right)\div \left( -2 \right)$

(10)$\left( -\dfrac {1} {6} a+\dfrac {2} {3} b \right)\div \left( -4 \right)$

(1)$12a\div 2$
$=12a\times \dfrac {1} {2}$
$=6a$

(2)$30x\div \left( -5 \right)$
$=30x\times\left( -\dfrac {1} {5} \right)$
$=-6x$

(3)$-24x\div 6$
$=-24x\times \dfrac {1} {6}$
$=-4x$

(4)$12x\div \dfrac {1} {3}$
$=12x\times 3$
$=36x$

(5)$20a\div \dfrac {4} {5}$
$=20a\times \dfrac {5} {4}$
$=5a\times 5$
$=25a$

(6)$\left( 6a+8 \right)\div 2$
$=\left( 6a+8 \right) \times \dfrac {1} {2}$
$=3a+4$

(7)$\left( 9x-12y+6 \right)\div \left( -3 \right)$
$=\left( 9x-12y+6 \right) \times \left( -\dfrac {1} {3} \right)$
$=-3x+4y-2$

(8)$\left( 4x-8y \right) \div \dfrac {1} {2}$
$=\left( 4x-8y \right) \times 2$
$=8x-16y$

(9)$\left( 8x+4y \right)\div \left( -2 \right)$
$=\left( 8x+4y \right)\times \left( -\dfrac {1} {2} \right)$
$=-4x-2y$

(10)$\left( -\dfrac {1} {6} a+\dfrac {2} {3} b \right)\div \left( -4 \right)$
$=\left( -\dfrac {1} {6} a+\dfrac {2} {3} b \right)\times \left( -\dfrac {1} {4} \right)$
$=\dfrac {1} {24} a-\dfrac {1} {6} b$

(8) ̌vZ܂傤B
(1)$\dfrac {a-b} {2} +\dfrac {a+2} {3}$

(2)$\dfrac {3x-y} {2} -\dfrac {x-4y} {4}$

(3)$\dfrac {5x-y} {3} -\dfrac {3x+y} {2}$

(4)$\dfrac {2a-b} {4} -\dfrac {a-2b} {6}$

(5)$\dfrac {3a+b+4} {5} -\dfrac {b+2a+4} {2}$

(6)$x-2y+\dfrac {x-4y} {3}$

(1)$\dfrac {a-b} {2} +\dfrac {a+2} {3}$
$=\dfrac {3\left( a-b \right) } {6} +\dfrac {2\left( a+2 \right) } {6}$
$=\dfrac {3\left( a-b \right)+2\left( a+2 \right) } {6}$
$=\dfrac {3a-3b+2a+4} {6}$
$=\dfrac {5a-3b+4} {6}$

(2)$\dfrac {3x-y} {2} -\dfrac {x-4y} {4}$
$=\dfrac {2\left( 3x-y \right) } {4} -\dfrac {x-4y} {4}$
$=\dfrac {2\left( 3x-y \right)-\left( x-4y \right) } {4}$
$=\dfrac {6x-2y-x+4y} {4}$
$=\dfrac {5x+2y} {4}$

(3)$\dfrac {5x-y} {3} -\dfrac {3x+y} {2}$
$=\dfrac {2\left( 5x-y \right) } {6} -\dfrac {3\left( 3x+y \right) } {6}$
$=\dfrac {2\left( 5x-y \right)-3\left( 3x+y \right) } {6}$
$=\dfrac {10x-2y-9x+3y} {6}$
$=\dfrac {x+y} {6}$

(4)$\dfrac {2a-b} {4} -\dfrac {a-2b} {6}$
$=\dfrac {3\left( 2a-b \right) } {12} -\dfrac {2\left( a-2b \right) } {12}$
$=\dfrac {3\left( 2a-b \right)-2\left( a-2b \right) } {12}$
$=\dfrac {6a-3b-2a+4b} {12}$
$=\dfrac {4a+b} {12}$

(5)$\dfrac {3a+b+4} {5} -\dfrac {b+2a+4} {2}$
$=\dfrac {2\left( 3a+b+4 \right) } {10} -\dfrac {5\left( b+2a+4 \right) } {10}$
$=\dfrac {2\left( 3a+b+4 \right)-5\left( b+2a+4 \right) } {10}$
$=\dfrac {6a+2b+8-5b-10a-20} {10}$
$=\dfrac {-4a-3b-12} {10}$

(6)$x-2y+\dfrac {x-4y} {3}$
$=\dfrac {3\left( x-2y \right) } {3} +\dfrac {x-4y} {3}$
$=\dfrac {3\left( x-2y \right)+x-4y} {3}$
$=\dfrac {3x-6y+x-4y} {3}$
$=\dfrac {4x-10y} {3}$

(9) ̌vZ܂傤B
(1)$4a\times 3b$

(2)$6x\times \left( -8y \right)$

(3)$\left( -7xy \right)\times 6z$

(4)$\left( -\dfrac {3} {4} a \right)\times \left( -\dfrac {2} {9} bc \right)$

(5)$5a\times \left( -a^2 \right)$

(6)$\left( -3x^2 y \right)\times 6xy$

(7)$\left( -2m \right)^4$

(8)$ab\times 5ab^2$

(9)$\dfrac {5} {8} xy\times \left( -2y \right)^3$

(10)$\left( -4xy \right)^2 \times \left( -\dfrac {3} {4} z \right)$

(1)$4a\times 3b$
$=12ab$

(2)$6x\times \left( -8y \right)$
$=-48xy$

(3)$\left( -7xy \right)\times 6z$
$=-42xyz$

(4)$\left( -\dfrac {3} {4} a \right)\times \left( -\dfrac {2} {9} bc \right)$
$=\left( -\dfrac {1} {2} a \right)\times \left( -\dfrac {1} {3} bc \right)$
$=\dfrac {1} {6} abc$

(5)$5a\times \left( -a^2 \right)$
$=-5a^3$

(6)$\left( -3x^2 y \right)\times 6xy$
$=-18x^3y^2$

(7)$\left( -2m \right)^4$
$=16m^4$

(8)$ab\times 5ab^2$
$=5a^2b^3$

(9)$\dfrac {5} {8} xy\times \left( -2y \right)^3$
$=\dfrac {5} {8} xy\times \left( -8y^3 \right)$
$=-5xy^4$

(10)$\left( -4xy \right)^2 \times \left( -\dfrac {3} {4} z \right)$
$=16x^2y^2 \times \left( -\dfrac {3} {4} z \right)$
$=-12x^2y^2 z$

(10) ̌vZ܂傤B
(1)$6ab\div 2a$

(2)$\left( -5xy \right) \div \dfrac {1} {2} x$

(3)$12xy\div \left( -4xy \right)$

(4)$\left( -24xy^2 \right) \div \left( -8xy \right)$

(5)$\dfrac {4} {5} a^4b^2 \div \left( -\dfrac {1} {2b} \right)$

(6)$a^2 b \div ab\times 5$

(7)$6a^2 \times ab\div \left( -3a \right)$

(8)$12x^3 \div \left( -4xy \right)\times y^2$

(9)$\left( -2x \right)^4 \times x \div \left( -2x \right)$

(10)$12a^2b^2 \times \left( -4b \right) \div \left( -8a \right)$

(1)$6ab\div 2a$
$= 6ab\times \dfrac {1} {2a}$
$=3b$

(2)$\left( -5xy \right) \div \dfrac {1} {2} x$
$= \left( -5xy \right) \times \dfrac {2} {x}$
$=-10y$

(3)$12xy\div \left( -4xy \right)$
$= 12xy\times \left( -\dfrac {1} {4xy} \right)$
$=-3$

(4)$\left( -24xy^2 \right) \div \left( -8xy \right)$
$= \left( -24xy^2 \right) \times \left( -\dfrac {1} {8xy} \right)$
$=3y$

(5)$\dfrac {4} {5} a^4b^2 \div \left( -\dfrac {1} {2b} \right)$
$= \dfrac {4} {5} a^4b^2 \times \left( -2b \right)$
$=-\dfrac {8} {5} a^4b^3$

(6)$a^2 b \div ab\times 5$
$= a^2 b\times \dfrac {1} {ab} \times 5$
$=5a$

(7)$6a^2 \times ab\div \left( -3a \right)$
$= 6a^2\times ab\times \left( -\dfrac {1} {3a} \right)$
$=2a^2 b$

(8)$12x^3 \div \left( -4xy \right)\times y^2$
$= 12x^3\times \left( -\dfrac {1} {4xy} \right) \times y^2$
$=3x^2 y$

(9)$\left( -2x \right)^4 \times x \div \left( -2x \right)$
$= 16x^4 \times x\times \left( -\dfrac {1} {2x} \right)$
$=-8x^4$

(10)$12a^2b^2 \times \left( -4b \right) \div \left( -8a \right)$
$= 12a^2b^2 \times \left( -4b \right) \times \left( -\dfrac {1} {8a} \right)$
$=6ab^3$

(11) ̎̒l߂܂傤B
(1)$a=-5$  ̂Ƃ
① $2a+5$
② $-a^2$

(2)$x=2$  , $y=-3$  ̂Ƃ
① $-5xy$
② $2x-y^2$

(3)$a=-2$  , $b=\dfrac {1} {3}$  ̂Ƃ
① $4\left(a+2b \right)+\left( a-5b \right)$
② $6a^2 b\div 3a$

(4)$a=2$  , $b=-1$  ̂Ƃ
① $3\left( 2a-5b \right)-4\left( a-3b \right)$
② $\left( -2a^2 b \right)^2 \times 4ab^2 \div \left( -8ab \right)$

(1)$a=-5$  ̂Ƃ
① $2a+5$
$=2\times \left( -5 \right)+5$
$=-5$

② $-a^2$
$=-\left( -5 \right)^2$
$=-25$

(2)$x=2$  , $y=-3$  ̂Ƃ
① $-5xy$
$=-5\times 2\times \left( -3 \right)$
$=30$

② $2x-y^2$
$=2\times 2-\left( -3 \right)^2$
$=4-9$
$=-5$

(3)$a=-2$  , $b=\dfrac {1} {3}$  ̂Ƃ
① $4\left(a+2b \right)+\left( a-5b \right)$
$=4a+8b+a-5b$
$=5a+3b$
$=5\times \left( -2 \right)+3\times \dfrac {1} {3}$
$=-10+1$
$=-9$

② $6a^2 b\div 3a$
$=6a^2 b\times \dfrac {1} {3a}$
$=2ab$
$=2\times \left( -2 \right)\times \dfrac {1} {3}$
$=-\dfrac {4} {3}$

(4)$a=2$  , $b=-1$  ̂Ƃ
① $3\left( 2a-5b \right)-4\left( a-3b \right)$
$=6a-15b-4a+12b$
$=2a-3b$
$=2\times 2-3\times \left( -1 \right)$
$=7$

② $\left( -2a^2 b \right)^2 \times 4ab^2 \div \left( -8ab \right)$
$=4a^4b^2 \times 4ab^2 \times \left( -\dfrac {1} {8ab} \right)$
$=2a^4b^3$
$=2a^4b^3$
$=2\times 2^4 \times \left( -1 \right)^3$
$=2\times 16\times \left( -1 \right)$
$=-31$