画像にある問題の中から、以下の問題を解きます。 (1) $3(x+5y) + 4(x-2y)$ (2) $5(2a-4b) + 6(-3a+5b)$ (3) $2(3x+2y) - 3(x+3y)$ (4) $7(4x-y) - 2(9x-7y)$ (5) $\frac{3x-4y}{5} + \frac{x+y}{2}$ (6) $\frac{a+3b}{8} - \frac{2a-5b}{4}$ (1) $-3(4x+3y) + 5(3x-2y)$ (2) $6(a+2b-1) - 3(2a+3b-2)$ (3) $\frac{1}{4}(4x-8y) + \frac{1}{3}(9x+3y)$ (4) $3a+b - \frac{2a-7b}{3}$ (1) $4a \times 7b$ (2) $5a^2 \times (-2a)$ (3) $(-6x)^2$ (4) $(-a)^2 \times (-7a^2)$ (1) $3ab \times 2c$ (2) $5xy \times (-x^2y)$ (3) $(-3x)^3$ (4) $(-a^2) \times (-6a)^2$ (1) $12ab \div 4b$ (2) $15x^2 \div (-3x)$

はい、承知いたしました。問題と解答を以下に示します。

1. 問題の内容

画像にある問題の中から、以下の問題を解きます。

(1) $3(x+5y) + 4(x-2y)$

(2) $5(2a-4b) + 6(-3a+5b)$

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

(4) $7(4x-y) - 2(9x-7y)$

(5) $\frac{3x-4y}{5} + \frac{x+y}{2}$

(6) $\frac{a+3b}{8} - \frac{2a-5b}{4}$

(1) $-3(4x+3y) + 5(3x-2y)$

(2) $6(a+2b-1) - 3(2a+3b-2)$

(3) $\frac{1}{4}(4x-8y) + \frac{1}{3}(9x+3y)$

(4) $3a+b - \frac{2a-7b}{3}$

(1) $4a \times 7b$

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

(3) $(-6x)^2$

(4) $(-a)^2 \times (-7a^2)$

(1) $3ab \times 2c$

(2) $5xy \times (-x^2y)$

(3) $(-3x)^3$

(4) $(-a^2) \times (-6a)^2$

(1) $12ab \div 4b$

(2) $15x^2 \div (-3x)$

2. 解き方の手順

順番に計算します。

(1) $3(x+5y) + 4(x-2y) = 3x + 15y + 4x - 8y = (3x+4x) + (15y-8y) = 7x + 7y$

(2) $5(2a-4b) + 6(-3a+5b) = 10a - 20b - 18a + 30b = (10a - 18a) + (-20b + 30b) = -8a + 10b$

(3) $2(3x+2y) - 3(x+3y) = 6x + 4y - 3x - 9y = (6x-3x) + (4y-9y) = 3x - 5y$

(4) $7(4x-y) - 2(9x-7y) = 28x - 7y - 18x + 14y = (28x - 18x) + (-7y + 14y) = 10x + 7y$

(5) $\frac{3x-4y}{5} + \frac{x+y}{2} = \frac{2(3x-4y)}{10} + \frac{5(x+y)}{10} = \frac{6x-8y+5x+5y}{10} = \frac{11x-3y}{10}$

(6) $\frac{a+3b}{8} - \frac{2a-5b}{4} = \frac{a+3b}{8} - \frac{2(2a-5b)}{8} = \frac{a+3b - 4a+10b}{8} = \frac{-3a+13b}{8}$

(1) $-3(4x+3y) + 5(3x-2y) = -12x - 9y + 15x - 10y = (-12x+15x) + (-9y-10y) = 3x - 19y$

(2) $6(a+2b-1) - 3(2a+3b-2) = 6a + 12b - 6 - 6a - 9b + 6 = (6a-6a) + (12b-9b) + (-6+6) = 3b$

(3) $\frac{1}{4}(4x-8y) + \frac{1}{3}(9x+3y) = x - 2y + 3x + y = (x+3x) + (-2y+y) = 4x - y$

(4) $3a+b - \frac{2a-7b}{3} = \frac{3(3a+b)}{3} - \frac{2a-7b}{3} = \frac{9a+3b-2a+7b}{3} = \frac{7a+10b}{3}$

(1) $4a \times 7b = 28ab$

(2) $5a^2 \times (-2a) = -10a^3$

(3) $(-6x)^2 = (-6x) \times (-6x) = 36x^2$

(4) $(-a)^2 \times (-7a^2) = a^2 \times (-7a^2) = -7a^4$

(1) $3ab \times 2c = 6abc$

(2) $5xy \times (-x^2y) = -5x^3y^2$

(3) $(-3x)^3 = (-3x) \times (-3x) \times (-3x) = -27x^3$

(4) $(-a^2) \times (-6a)^2 = (-a^2) \times (36a^2) = -36a^4$

(1) $12ab \div 4b = \frac{12ab}{4b} = 3a$

(2) $15x^2 \div (-3x) = \frac{15x^2}{-3x} = -5x$

3. 最終的な答え

(1) $7x+7y$

(2) $-8a+10b$

(3) $3x-5y$

(4) $10x+7y$

(5) $\frac{11x-3y}{10}$

(6) $\frac{-3a+13b}{8}$

(1) $3x-19y$

(2) $3b$

(3) $4x-y$

(4) $\frac{7a+10b}{3}$

(1) $28ab$

(2) $-10a^3$

(3) $36x^2$

(4) $-7a^4$

(1) $6abc$

(2) $-5x^3y^2$

(3) $-27x^3$

(4) $-36a^4$

(1) $3a$

(2) $-5x$