1.次の多項式の項と次数を答えなさい。
(1)\(x+3y\)
項:\(x,3y\)
次数:1
(2)\(2x+xy\)
項:\(2x,xy\)
次数:2
(3)\(2a-5b+1\)
項:\(2a,-5b,1\)
次数:1
(4)\(a^2-4ab+4b^2\)
項:\(a^2,-4ab,4b^2\)
次数:2
(5)\(2x+7y\)
項:\(2x,7y\)
次数:1
(6)\(3xy-x+1\)
項:\(3xy,-x,1\)
次数:2
(7)\(2a^2+3ab+2b-5\)
項:\(2a^2,3ab,2b,-5\)
次数:2
(8)\(x^2-6x^2y+3y\)
項:\(x^2,-6x^2y,3y\)
次数:3
2.次の式を計算しなさい。
(1)\(x^2+6x+2x^2-3x\)
\(=(1+2)x^2+(6-3)x\)
\(=3x^2+3x\)
(2)\(2x+4xy-7x-2xy\)
\(=(2-7)x+(4-2)xy\)
\(=-5x+2xy\)
(3)\(-2x+5y+8x-3y\)
\(=(-2+8)x+(5-3)y\)
\(=6x+2y\)
(4)\(9x^2+3xy-2x^2-7xy\)
\(=(9-2)x^2+(3-7)xy\)
\(=7x^2-4xy\)
(5)\(4x+3y-x\)
\(=(4-1)x+3y\)
\(=3x+3y\)
(6)\(5a-2b+2a-4b+7\)
\(=(5+2)a+(-2-4)b+7\)
\(=7a-6b+7\)
(7)\(a^2-0.4a+2a^2+0.5a\)
\(=(1+2)a^2+(-0.4+0.5)a\)
\(=3a^2+0.1a\)
(8)\(\frac{2}{3}x-y-\frac{1}{6}x+3y\)
\(=(\frac{2}{3}-\frac{1}{6})x+(-1+3)y\)
\(=\frac{1}{2}x+2y\)
(9)\(3x-2y-x\)
\(=(3-1)x-2y\)
\(=2x-2y\)
(10)\(-4a+2b+3a-b\)
\(=(-4+3)a+(2-1)b\)
\(=-a+b\)
(11)\(9x^2-2xy+5x^2+3xy\)
\(=(9+5)x^2+(-2+3)xy\)
\(=14x^2+xy\)
(12)\(a^2+\frac{ab}{4}-3a^2+\frac{ab}{3}\)
\(=(1-3)a^2+(\frac{1}{4}+\frac{1}{3})ab\)
\(=-2a^2+\frac{7}{12}ab\)
(13)\(x+3y-y\)
\(=x+(3-1)y\)
\(=x+2y\)
(14)\(3a-4b-2a+b\)
\(=(3-2)a+(-4+1)b\)
\(=a-3b\)
(15)\(-7x+2y+6x-2y\)
\(=(-7+6)x+(2-2)y\)
\(=-x\)
(16)\(6a^2+a-7a^2-2a\)
\(=(6-7)a^2+(1-2)a\)
\(=-a^2-a\)
(17)\((2x+y)+(5x+6y)\)
\(=2x+y+5x+6y\)
\(=7x+7y\)
(18)\((3a-4b)+(-2a+7b)\)
\(=3a-4b-2a+7b\)
\(=a+3b\)
(19)\((-2x+4y)+(10x-6y)\)
\(=-2x+4y+10x-6y\)
\(=8x-2y\)
(20)\((5x^2+4x-2)+(x^2-3x+1)\)
\(=5x^2+4x-2+x^2-3x+1\)
\(=6x^2+x-1\)
(21)\((4x+7y)-(3x+y)\)
\(=4x+7y-3x-y\)
\(=x+6y\)
(22)\((2x+5y)-(4x-3y)\)
\(=2x+5y-4x+3y\)
\(=-2x+8y\)
(23)\((6a-2b)-(-3a+4b)\)
\(=6a-2b+3a-4b\)
\(=9a-6b\)
(24)\((x^2-2x-3)-(6x^2-4x+1)\)
\(=x^2-2x-3-6x^2+4x-1\)
\(=-5x^2+2x-4\)
(25)\((x+5y)+(2x-7y)\)
\(=x+5y+2x-7y\)
\(=3x-2y\)
(26)\((2a-b)-(6a-5b)\)
\(=2a-b-6a+5b\)
\(=-4a+4b\)
(27)\((2a-b)+(a+5b)\)
\(=2a-b+a+5b\)
\(=3a+4b\)
(28)\((x-y)-(-7x+2y)\)
\(=x-y+7x-2y\)
\(=8x-3y\)
(29)\((6x-3y)+(2x+5y)\)
\(=6x-3y+2x+5y\)
\(=8x+2y\)
(30)\((2a-b)+(-3a+2b)\)
\(=2a-b-3a+2b\)
\(=-a+b\)
(31)\((2x^2+xy-y^2)+(-3x^2-2xy+3y^2)\)
\(=2x^2+xy-y^2-3x^2-2xy+3y^2\)
\(=-x^2-xy+2y^2\)
(32)\((3x-4y)-(-2x+y)\)
\(=3x-4y+2x-y\)
\(=5x-5y\)
(33)\((a+2b)-(3a-4b)\)
\(=a+2b-3a+4b\)
\(=-2a+6b\)
(34)\((x^2-2xy+y^2)-(-x^2+xy-4y^2)\)
\(=x^2-2xy+y^2+x^2-xy+4y^2\)
\(=2x^2-3xy+5y^2\)
(35)\((7x-5y)+(-5x+7y)\)
\(=7x-5y-5x+7y\)
\(=2x+2y\)
(36)\((3a-b)-(-2a+5b)\)
\(=3a-b+2a-5b\)
\(=5a-6b\)
(37)\((\frac{x}{3}+\frac{y}{2})+(\frac{x}{2}-\frac{5}{2}y)\)
\(=\frac{x}{3}+\frac{y}{2}+\frac{x}{2}-\frac{5}{2}y\)
\(=\frac{5}{6}x-2y\)
(38)\((\frac{x}{2}-y)-(\frac{2}{3}x-\frac{y}{3})\)
\(=\frac{x}{2}-y-\frac{2}{3}x+\frac{y}{3}\)
\(=-\frac{1}{6}x-\frac{2}{3}y\)
(39)\((3x-y)+(2x+5y)\)
\(=3x-y+2x+5y\)
\(=5x+4y\)
(40)\((a^2+2ab-b^2)+(a^2-ab+b^2)\)
\(=a^2+2ab-b^2+a^2-ab+b^2\)
\(=2a^2+ab\)
(41)\((8x-5y)-(4x-6y)\)
\(=8x-5y-4x+6y\)
\(=4x+y\)
(42)\((2x^2+2x-4)-(x^2+3x-5)\)
\(=2x^2+2x-4-x^2-3x+5\)
\(=x^2-x+1\)
(43)\((3x-5y)+(2x+3y)\)
\(=3x-5y+2x+3y\)
\(=5x-2y\)
(44)\((9a-10b)-(6a-7b)\)
\(=9a-10b-6a+7b\)
\(=3a-3b\)
(45)\(3x×2y\)
\(=6xy\)
(46)\(4a×(-3b)\)
\(=-12ab\)
(47)\((-x)×(-5y)\)
\(=5xy\)
(48)\((-7a)×2a\)
\(=-14a^2\)
(49)\(\frac{1}{3}x×(-6y)\)
\(=-2xy\)
(50)\((-4ab)×(-\frac{1}{8}c)\)
\(=\frac{1}{2}abc\)
(51)\(12xy÷2y\)
\(=\frac{12xy}{2y}\)
\(=6x\)
(52)\(8x^2÷4x\)
\(=\frac{8x^2}{4x}\)
\(=2x\)
(53)\(2ab÷\frac{1}{2}b\)
\(=\frac{2ab×2}{b}\)
\(=4a\)
(54)\(4xy÷\frac{8}{5}x\)
\(=\frac{4xy×5}{8x}\)
\(=\frac{5}{2}y\)
(55)\(3x×2xy÷6y\)
\(=\frac{3x×2xy}{6y}\)
\(=x^2\)
(56)\(20a^2b^2÷(-5b)÷2ab\)
\(=-\frac{20a^2b^2}{5b×2ab}\)
\(=-2a\)
(57)\(16x^2y÷8y\)
\(=\frac{16x^2y}{8y}\)
\(=2x^2\)
(58)\((-21a^2b^2)÷(-6ab)\)
\(=\frac{21a^2b^2}{6ab}\)
\(=\frac{7}{2}ab\)
(59)\(9x^2y÷(-\frac{3}{4}x)\)
\(=-\frac{9x^2y×4}{3x}\)
\(=-12xy\)
(60)\((-\frac{4}{3}a^2b)÷\frac{7}{6}ab\)
\(=-\frac{4a^2b×6}{3×7ab}\)
\(=-\frac{8}{7}a\)
(61)\(3(a+2b)\)
\(=3a+6b\)
(62)\(-2(5x+2y)\)
\(=-10x-4y\)
(63)\((a-5b)×\frac{1}{5}\)
\(=\frac{1}{5}a-b\)
(64)\(6(\frac{x}{2}-\frac{y}{3})\)
\(=3x-2y\)
(65)\((8a+4b)÷2\)
\(=4a+2b\)
(66)\((3x-12y)÷(-3)\)
\(=-x+4y\)
(67)\((-7a-21b)÷(-7)\)
\(=a+3b\)
(68)\((3x-6y)÷\frac{3}{2}\)
\(=(3x-6y)×\frac{2}{3}\)
\(=2x-4y\)
(69)\(2(2x-y)+3(x+4y)\)
\(=4x-2y+3x+12y\)
\(=7x+10y\)
(70)\(5(3x+2y)-2(5x+4y)\)
\(=15x+10y-10x-8y\)
\(=5x+2y\)
(71)\(2(2a+3b)+3(a-4b)\)
\(=4a+6b+3a-12b\)
\(=7a-6b\)
(72)\(4(3x-2y)-7(2x-y)\)
\(=12x-8y-14x+7y\)
\(=-2x-y\)
(73)\(6(x^2-x+2)+3(x^2+2x-2)\)
\(=6x^2-6x+12+3x^2+6x-6\)
\(=9x^2+6\)
(74)\(2(2x^2+3x-5)-3(x^2+3x-2)\)
\(=4x^2+6x-10-3x^2-9x+6\)
\(=x^2-3x-4\)
(75)\((6x-2y)-(x-7y)\)
\(=6x-2y-x+7y\)
\(=5x+5y\)
(76)\(2(3x-y)+4(-x+2y)\)
\(=6x-2y-4x+8y\)
\(=2x+6y\)
(77)\(2(x+5y)+3(x-3y)\)
\(=2x+10y+3x-9y\)
\(=5x+y\)
(78)\(6(x-2y)-4(x-3y)\)
\(=6x-12y-4x+12y\)
\(=2x\)
(79)\(7(-2x+y)+4(3x-4y)\)
\(=-14x+7y+12x-16y\)
\(=-2x-9y\)
(80)\(3(2a-3b)-5(a-2b)\)
\(=6a-9b-5a+10b\)
\(=a+b\)
(81)\(2(3a+2b)+4(a-3b)\)
\(=6a+4b+4a-12b\)
\(=10a-8b\)
(82)\(6(x-2y)-5(-2x+y)\)
\(=6x-12y+10x-5y\)
\(=16x-17y\)
(83)\(-3(2a+3b)-(7a-4b)\)
\(=-6a-9b-7a+4b\)
\(=-13a-5b\)
(84)\(-2(3x-2y)+3(-x+2y)\)
\(=-6x+4y-3x+6y\)
\(=-9x+10y\)
(85)\(5(4x+2y)-2(-5x-4y)\)
\(=20x+10y+10x+8y\)
\(=30x+18y\)
(86)\(3(-2a+5b)+4(a+6b)\)
\(=-6a+15b+4a+24b\)
\(=-2a+39b\)
(87)\(\frac{x+2y}{3}+\frac{2x-y}{2}\)
\(=\frac{2(x+2y)+3(2x-y)}{6}\)
\(=\frac{2x+4y+6x-3y}{6}\)
\(=\frac{8x+y}{6}\)
(88)\(\frac{3a-2b}{4}-\frac{a-2b}{2}\)
\(=\frac{3a-2b-2(a-2b)}{4}\)
\(=\frac{3a-2b-2a+4b}{4}\)
\(=\frac{a+2b}{4}\)
(89)\(3x-y+\frac{x+4y}{3}\)
\(=\frac{3(3x-y)+(x+4y)}{3}\)
\(=\frac{9x-3y+x+4y}{3}\)
\(=\frac{10x+y}{3}\)
(90)\(\frac{2a+b}{2}-\frac{3a-b}{5}\)
\(=\frac{5(2a+b)-2(3a-b)}{10}\)
\(=\frac{10a+5b-6a+2b}{10}\)
\(=\frac{4a+7b}{10}\)
(91)\(\frac{2a+3b}{7}+a-2b\)
\(=\frac{(2a+3b)+7(a-2b)}{7}\)
\(=\frac{2a+3b+7a-14b}{7}\)
\(=\frac{9a-11b}{7}\)
(92)\(\frac{5x-7y}{8}-\frac{2x-3y}{2}\)
\(=\frac{(5x-7y)-4(2x-3y)}{8}\)
\(=\frac{5x-7y-8x+12y}{8}\)
\(=\frac{-3x+5y}{8}\)
3.\(x=-2,y=4\)のとき、次の式の値を求めなさい。
(1)\(2(3x+y)-3(2x+4y)\)
\(=6x+2y-6x-12y\)
\(=-10y\)
\(=-10×4\)
\(=-40\)
(2)\(28x^2y^2÷(-2y)÷7x\)
\(=-\frac{28x^2y^2}{2y×7x}\)
\(=-2y\)
\(=-2×(-2)×4\)
\(=16\)
4.\(x=4,y=-6\)のとき、次の式の値を求めなさい。
(1)\(5(2x-3y)-7(x-2y)\)
\(=10x-15y-7x+14y\)
\(=3x-y\)
\(=3×4-(-6)\)
\(=18\)
(2)\(3x^3y×(-8y)÷(-6x^2y)\)
\(=\frac{3x^3y×8y}{6x^2y}\)
\(=4xy\)
\(=4×4×(-6)\)
\(=-96\)