(1)\(2x-3\)

  項：\(2x\)  ,\(-3\)
 \(x\)  の係数は\(2\)

(2)\(-4x+\dfrac {1} {2} y\)

  項：\(-4x\)  ,\(\dfrac {1} {2} y\)
 \(x\)  の係数は\(-4\)  ,\(y\)  の係数は\(\dfrac {1} {2} \)

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

  項：\(a\)  ,\(-2b\)  ,\(3cd\)
 \(a\)  の係数は\(1\)  ,\(b\)  の係数は\(-2\)  ,\(cd\)  の係数は\(3\)

(4)\(-5x^2 -y^2 -5\)

  項：\(-5x^2\)  ,\(-y^2\)  ,\(-5\)
 \(x^2\)  の係数は\(-5\)  ,\(y^2\)  の係数は\(-1\)

(1) ２
(2) ３
(3) ６
(4) ２
(5) ３

(1) ２ （\(3x^2\)  の文字数 ）
(2) ４ （\(-ab^3\)  の文字数 ）
(3) ２ （ どの項の文字数も\(2\)  ）
(4) ５ （\(x^5\)  の文字数 ）
(5) ６ （\(4a^3 bc^2\)  の文字数 ）

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

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

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

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

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

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

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

(1)\(a=-5\)  のとき
① \(2a+5\)
\(=2\times \left( -5 \right)+5 \)
\(=-5\)

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

(2)\(x=2\)  , \(y=-3\)  のとき
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)\(a=-2\)  , \(b=\dfrac {1} {3} \)  のとき
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)\(a=2\)  , \(b=-1\)  のとき
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 \(\left( -2a^2 b \right)^2 \times 4ab^2 \div \left( -8ab \right) \)
\(=4a^4b^2 \times 4ab^2 \times \left( -\dfrac {1} {8ab}  \right) \)
\(=2a^4b^3\)
\(=2a^4b^3\)
\(=2\times 2^4 \times \left( -1 \right)^3 \)
\(=2\times 16\times \left( -1 \right) \)
\(=-31\)