【中学3年数学】1-1 式の展開｜問題集
1.次の式を計算しなさい。
(1)\(3a(5a+2b)\)
\(=15a^2+6ab\)
(2)\(-4x(6x-5y)\)
\(=-24x^2+20xy\)
(3)\((2x-3y)×6y\)
\(=12xy-18y^2\)
(4)\(\displaystyle \left(\frac{2}{3}a+\frac{3}{4}b\right)×12b\)
\(=8ab+9b^2\)
(5)\((12ab+6a)÷3a\)
\(=4b+2\)
(6)\((20ax-5bx)÷5x\)
\(=4a-b\)
(7)\((16xy+4x^2)÷(-4x)\)
\(=-4y-x\)
(8)\((3x^2-9xy)÷(-3x)\)
\(=-x+3y\)
(9)\(\displaystyle (-9a^2+15ab)÷\frac{3}{4}a\)
\(\displaystyle =(-9a^2+15ab)×\frac{4}{3a}\)
\(=-12a+20b\)
\(=-12a+20b\)
(10)\(\displaystyle (12x^3-4x^2)÷\left(-\frac{4}{7}x^2\right)\)
\(\displaystyle =(12x^3-4x^2)×\left(-\frac{7}{4x^2}\right)\)
\(=-21x+7\)
\(=-21x+7\)
(11)\(\displaystyle (20xy-15y^2)÷\frac{5}{2}y\)
\(\displaystyle =(20xy-15y^2)×\frac{2}{5y}\)
\(=8x-6y\)
\(=8x-6y\)
(12)\(4x(2x+5y)\)
\(=8x^2+20xy\)
(13)\(3a(a-7b)\)
\(=3a^2-21ab\)
(14)\(-2x(6x-9y)\)
\(=-12x^2+18xy\)
(15)\((15xy+10x^2)÷5x\)
\(=3y+2x\)
(16)\((7a^2+21ab)÷(-7a)\)
\(=-a-3b\)
(17)\(\displaystyle (12x^2-18xy)÷\frac{3}{2}x\)
\(\displaystyle =(12x^2-18xy)×\frac{2}{3x}\)
\(=8x-12y\)
\(=8x-12y\)
(18)\(2x(4x-7y)\)
\(=8x^2-14xy\)
(19)\((6a-3b)×(-5a)\)
\(=-30a^2+15ab\)
(20)\((18x^2+21xy)÷3x\)
\(=6x+7y\)
(21)\(\displaystyle (63ax-9bx)÷\frac{9}{4}x\)
\(\displaystyle =(63ax-9bx)×\frac{4}{9x}\)
\(=28a-4b\)
\(=28a-4b\)
(22)\(2x(2x+1)+5x(x-4)\)
\(=4x^2+2x+5x^2-20x\)
\(=9x^2-18x\)
\(=9x^2-18x\)
(23)\(-3m(m-2n)+2m(7m-n)\)
\(=-3m^2+6mn+14m^2-2mn\)
\(=11m^2+4mn\)
\(=11m^2+4mn\)
(24)\(6a(3a-10b)-4b(9a-2b)\)
\(=18a^2-60ab-36ab+8b^2\)
\(=18a^2-96ab+8b^2\)
\(=18a^2-96ab+8b^2\)
(25)\(\displaystyle \frac{a}{3}(6a-3b)-\frac{b}{2}(4a+10b)\)
\(=2a^2-ab-2ab-5b^2\)
\(=2a^2-3ab-5b^2\)
\(=2a^2-3ab-5b^2\)
(26)\(\displaystyle \frac{x}{4}(12x-8y)+\frac{y}{5}(5x+20y)\)
\(=3x^2-2xy+xy+4y^2\)
\(=3x^2-xy+4y^2\)
\(=3x^2-xy+4y^2\)
(27)\(\displaystyle -\frac{x}{2}(10x-12y)+\frac{y}{7}(21x-7y)\)
\(=-5x^2+6xy+3xy-y^2\)
\(=-5x^2+9xy-y^2\)
\(=-5x^2+9xy-y^2\)
(28)\(-4a(3a+b)+6b(2a-5b)\)
\(=-12a^2-4ab+12ab-30b^2\)
\(=-12a^2+8ab-30b^2\)
\(=-12a^2+8ab-30b^2\)
(29)\(5x(6x-3y)-2y(8x+y)\)
\(=30x^2-15xy-16xy-2y^2\)
\(=30x^2-31xy-2y^2\)
\(=30x^2-31xy-2y^2\)
(30)\(\displaystyle 12a\left(\frac{a}{3}+\frac{b}{4}\right)\)
\(=4a^2+3ab\)
(31)\((x+4)(y+7)\)
\(=xy+7x+4y+28\)
(32)\((x-5)(y+3)\)
\(=xy+3x-5y-15\)
(33)\((x+8)(2y-5)\)
\(=2xy-5x+16y-40\)
(34)\((2x-5)(4y-3)\)
\(=8xy-6x-20y+15\)
(35)\((3x+5)(x+3)\)
\(=3x^2+9x+5x+15\)
\(=3x^2+14x+15\)
\(=3x^2+14x+15\)
(36)\((5a+2)(a-6)\)
\(=5a^2-30a+2a-12\)
\(=5a^2-28a-12\)
\(=5a^2-28a-12\)
(37)\((5x-4)(2x+3)\)
\(=10x^2+15x-8x-12\)
\(=10x^2+7x-12\)
\(=10x^2+7x-12\)
(38)\((3a-7)(4a-8)\)
\(=12a^2-24a-28a+56\)
\(=12a^2-52a+56\)
\(=12a^2-52a+56\)
(39)\((a-6)(a-b+8)\)
\(=a^2-ab+8a-6a+6b-48\)
\(=a^2-ab+2a+6b-48\)
\(=a^2-ab+2a+6b-48\)
(40)\((2x+3y-1)(x+y)\)
\(=2x^2+2xy+3xy+3y^2-x-y\)
\(=2x^2+5xy+3y^2-x-y\)
\(=2x^2+5xy+3y^2-x-y\)
(41)\((x+2)(y-7)\)
\(=xy-7x+2y-14\)
(42)\((x+2)(x+5)\)
\(=x^2+(2+5)x+2×5\)
\(=x^2+7x+10\)
\(=x^2+7x+10\)
(43)\((x+8)(x+1)\)
\(=x^2+(8+1)x+8×1\)
\(=x^2+9x+8\)
\(=x^2+9x+8\)
(44)\((x+6)(x+7)\)
\(=x^2+(6+7)x+6×7\)
\(=x^2+13x+42\)
\(=x^2+13x+42\)
(45)\((x+9y)(x+4y)\)
\(=x^2+(9y+4y)x+9y×4y\)
\(=x^2+13xy+36y^2\)
\(=x^2+13xy+36y^2\)
(46)\((x+5)(x-3)\)
\(=x^2+(5-3)x+5×(-3)\)
\(=x^2+2x-15\)
\(=x^2+2x-15\)
(47)\((x-7)(x+4)\)
\(=x^2+(-7+4)x-7×4\)
\(=x^2-3x-28\)
\(=x^2-3x-28\)
(48)\((x-3)(x-9)\)
\(=x^2+(-3-9)x-3×(-9)\)
\(=x^2-12x+27\)
\(=x^2-12x+27\)
(49)\((x-5)(x-6)\)
\(=x^2+(-5-6)x-5×(-6)\)
\(=x^2-11x+30\)
\(=x^2-11x+30\)
(50)\(\displaystyle \left(x+\frac{3}{2}\right)\left(x-\frac{1}{2}\right)\)
\(\displaystyle =x^2+\left(\frac{3}{2}-\frac{1}{2}\right)x+\frac{3}{2}×\left(-\frac{1}{2}\right)\)
\(\displaystyle =x^2+x-\frac{3}{4}\)
\(\displaystyle =x^2+x-\frac{3}{4}\)
(51)\((x-2y)(x+6y)\)
\(=x^2+(-2y+6y)x-2y×6y\)
\(=x^2+4xy-12y^2\)
\(=x^2+4xy-12y^2\)
(52)\((3x+7)(3x+1)\)
\(=(3x)^2+(7+1)×3x+7×1\)
\(=9x^2+24x+7\)
\(=9x^2+24x+7\)
(53)\((4x+1)(4x-7)\)
\(=(4x)^2+(1-7)×4x+1×(-7)\)
\(=16x^2-24x-7\)
\(=16x^2-24x-7\)
(54)\((2x-3)(2x+8)\)
\(=(2x)^2+(-3+8)×2x-3×8\)
\(=4x^2+10x-24\)
\(=4x^2+10x-24\)
(55)\((-x+6y)(-x+4y)\)
\(=(-x)^2+(6y+4y)×(-x)+6y×4y\)
\(=x^2-10xy+24y^2\)
\(=x^2-10xy+24y^2\)
(56)\((x+3)(x+6)\)
\(=x^2+(3+6)x+3×6\)
\(=x^2+9x+18\)
\(=x^2+9x+18\)
(57)\((x-6)(x+10)\)
\(=x^2+(-6+10)x-6×10\)
\(=x^2+4x-60\)
\(=x^2+4x-60\)
(58)\((x-6)(x-1)\)
\(=x^2+(-6-1)x-6×(-1)\)
\(=x^2-7x+6\)
\(=x^2-7x+6\)
(59)\((x+8)(x-2)\)
\(=x^2+(8-2)x+8×(-2)\)
\(=x^2+6x-16\)
\(=x^2+6x-16\)
(60)\((x-5)(x+4)\)
\(=x^2+(-5+4)x-5×4\)
\(=x^2-x-20\)
\(=x^2-x-20\)
(61)\((4x-3)(4x+5)\)
\(=(4x)^2+(-3+5)×4x-3×5\)
\(=16x^2+8x-15\)
\(=16x^2+8x-15\)
(62)\((2a+7)(2a+1)\)
\(=(2a)^2+(7+1)×2a+7×1\)
\(=4a^2+16a+7\)
\(=4a^2+16a+7\)
(63)\((x+6)(x+9)\)
\(=x^2+(6+9)x+6×9\)
\(=x^2+15x+54\)
\(=x^2+15x+54\)
(64)\((x-11)(x+3)\)
\(=x^2+(-11+3)x-11×3\)
\(=x^2-8x-33\)
\(=x^2-8x-33\)
(65)\((2x-5)(2x-7)\)
\(=(2x)^2+(-5-7)×2x-5×(-7)\)
\(=4x^2-24x+35\)
\(=4x^2-24x+35\)
(66)\((x+2)^2\)
\(=x^2+2×2x+2^2\)
\(=x^2+4x+4\)
\(=x^2+4x+4\)
(67)\((x+10)^2\)
\(=x^2+2×10x+10^2\)
\(=x^2+20x+100\)
\(=x^2+20x+100\)
(68)\((x-7)^2\)
\(=x^2-2×7x+7^2\)
\(=x^2-14x+49\)
\(=x^2-14x+49\)
(69)\((a-8)^2\)
\(=a^2-2×8a+8^2\)
\(=a^2-16a+64\)
\(=a^2-16a+64\)
(70)\(\displaystyle \left(4x-\frac{1}{3}\right)^2\)
\(\displaystyle =(4x)^2-2×\frac{1}{3}×4x+\left(\frac{1}{3}\right)^2\)
\(\displaystyle =16x^2-\frac{8}{3}x+\frac{1}{9}\)
\(\displaystyle =16x^2-\frac{8}{3}x+\frac{1}{9}\)
(71)\((3x-5y)^2\)
\(=(3x)^2-2×3x×5y+(5y)^2\)
\(=9x^2-30xy+25y^2\)
\(=9x^2-30xy+25y^2\)
(72)\((a-3)^2\)
\(=a^2-2×3a+3^2\)
\(=a^2-6a+9\)
\(=a^2-6a+9\)
(73)\((x+5)^2\)
\(=x^2+2×5x+5^2\)
\(=x^2+10x+25\)
\(=x^2+10x+25\)
(74)\((3a-8)^2\)
\(=(3a)^2-2×8×3a+8^2\)
\(=9a^2-48a+64\)
\(=9a^2-48a+64\)
(75)\((5a+2)^2\)
\(=(5a)^2+2×2×5a+2^2\)
\(=25a^2+20a+4\)
\(=25a^2+20a+4\)
(76)\((x-6)^2\)
\(=x^2-2×6x+6^2\)
\(=x^2-12x+36\)
\(=x^2-12x+36\)
(77)\((4x-3)^2\)
\(=(4x)^2-2×3×4x+3^2\)
\(=16x^2-24x+9\)
\(=16x^2-24x+9\)
(78)\((x+7y)^2\)
\(=x^2+2×7xy+(7y)^2\)
\(=x^2+14xy+49y^2\)
\(=x^2+14xy+49y^2\)
(79)\((x+7)(x-7)\)
\(=x^2-7^2\)
\(=x^2-49\)
\(=x^2-49\)
(80)\((x-3)(x+3)\)
\(=x^2-3^2\)
\(=x^2-9\)
\(=x^2-9\)
(81)\((6+x)(6-x)\)
\(=6^2-x^2\)
\(=36-x^2\)
\(=36-x^2\)
(82)\((2a-5)(2a+5)\)
\(=(2a)^2-5^2\)
\(=4a^2-25\)
\(=4a^2-25\)
(83)\(\displaystyle \left(2x+\frac{2}{3}\right)\left(2x-\frac{2}{3}\right)\)
\(\displaystyle =(2x)^2-\left(\frac{2}{3}\right)^2\)
\(\displaystyle =4x^2-\frac{4}{9}\)
\(\displaystyle =4x^2-\frac{4}{9}\)
(84)\((4x-5y)(4x+5y)\)
\(=(4x)^2-(5y)^2\)
\(=16x^2-25y^2\)
\(=16x^2-25y^2\)
(85)\((x+9)(x-9)\)
\(=x^2-9^2\)
\(=x^2-81\)
\(=x^2-81\)
(86)\((7a-2)(7a+2)\)
\(=(7a)^2-2^2\)
\(=49a^2-4\)
\(=49a^2-4\)
(87)\((-x-6)(-x+6)\)
\(=(-x)^2-6^2\)
\(=x^2-36\)
\(=x^2-36\)
(88)\((x+5)(x-3)+(x+8)(x+2)\)
\(=x^2+2x-15+x^2+10x+16\)
\(=2x^2+12x+1\)
\(=2x^2+12x+1\)
(89)\((x-4)^2-(x+7)(x+1)\)
\(=x^2-8x+16-(x^2+8x+7)\)
\(=-16x+9\)
\(=-16x+9\)
(90)\((x-2)(x+2)+2(x+9)^2\)
\(=x^2-4+2(x^2+18x+81)\)
\(=x^2-4+2x^2+36x+162\)
\(=3x^2+36x+158\)
\(=x^2-4+2x^2+36x+162\)
\(=3x^2+36x+158\)
(91)\((x+y+1)^2\)
\(=(x+y)^2+2(x+y)+1\)
\(=x^2+2xy+y^2+2x+2y+1\)
\(=x^2+2xy+y^2+2x+2y+1\)
(92)\((x+y-3)(x+y+3)\)
\(=(x+y)^2-3^2\)
\(=x^2+2xy+y^2-9\)
\(=x^2+2xy+y^2-9\)
(93)\((x-1)^2-5x(x+8)\)
\(=x^2-2x+1-5x^2-40x\)
\(=-4x^2-42x+1\)
\(=-4x^2-42x+1\)
(94)\((x+4)(x-6)-(x+3)^2\)
\(=x^2-2x-24-(x^2+6x+9)\)
\(=-8x-33\)
\(=-8x-33\)
(95)\((x-2)(x+10)+(x+5)(x-12)\)
\(=x^2+8x-20+x^2-7x-60\)
\(=2x^2+x-80\)
\(=2x^2+x-80\)
(96)\((a+3b-6)(a+3b+6)\)
\(=(a+3b)^2-6^2\)
\(=a^2+6ab+9b^2-36\)
\(=a^2+6ab+9b^2-36\)
(97)\(2(x+y-4)^2\)
\(=2\{(x+y)^2-8(x+y)+16\}\)
\(=2(x^2+2xy+y^2-8x-8y+16)\)
\(=2x^2+4xy+2y^2-16x-16y+32\)
\(=2(x^2+2xy+y^2-8x-8y+16)\)
\(=2x^2+4xy+2y^2-16x-16y+32\)
(98)\((x-3y-2)(x-3y+6)\)
\(=(x-3y)^2+4(x-3y)-12\)
\(=x^2-6xy+9y^2+4x-12y-12\)
\(=x^2-6xy+9y^2+4x-12y-12\)
(99)\((2x+1)^2-3(x+7)(x-6)+2x^2\)
\(=4x^2+4x+1-3(x^2+x-42)+2x^2\)
\(=4x^2+4x+1-3x^2-3x+126+2x^2\)
\(=3x^2+x+127\)
\(=4x^2+4x+1-3x^2-3x+126+2x^2\)
\(=3x^2+x+127\)
次の学習に進もう！