与えられた多項式の計算問題を解きます。具体的には、 (1) $2x-y+3x-5y$ (2) $-3x^2-4x+4x^2+6x$ (3) $7a+2b+5-9a+b$ (4) $(3a+2b)+(a-3b)$ (5) $(6x-5y)+(-x+7y)$ (6) $(x^2+5x-2)+(2x^2-x+3)$ (7) $(4a+3b)-(-2a-b)$ (8) $(3x-2y-2)-(x-9y-2)$ (9) $2a+5b + (4a-5b)$ (10) $(-3x-5y+1)+(x-2y-6)$ (11) $(8x-3y) - (4x+3y)$ (12) $(7x-y) - (2x-5y+10)$ (13) $4(3x-y)$ (14) $-6(2a-5b)$ (15) $12(\frac{x}{3}+\frac{y}{6})$ (16) $(15a-18b) \div 3$ (17) $(24x+16y) \div (-8)$ (18) $5(a-2b)+4(2a-b)$ (19) $6(x+y)-2(x+2y)$ (20) $-3(2a+4b-5)+2(3a+6b-1)$ (21) $\frac{1}{4}(8x-4y)+\frac{1}{2}(6x+8y)$ (22) $\frac{1}{8}(x+3y)-\frac{1}{6}(2x+y)$

1. 問題の内容

与えられた多項式の計算問題を解きます。具体的には、

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

(2) $-3x^2-4x+4x^2+6x$

(3) $7a+2b+5-9a+b$

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

(5) $(6x-5y)+(-x+7y)$

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

(7) $(4a+3b)-(-2a-b)$

(8) $(3x-2y-2)-(x-9y-2)$

(9) $2a+5b + (4a-5b)$

(10) $(-3x-5y+1)+(x-2y-6)$

(11) $(8x-3y) - (4x+3y)$

(12) $(7x-y) - (2x-5y+10)$

(13) $4(3x-y)$

(14) $-6(2a-5b)$

(15) $12(\frac{x}{3}+\frac{y}{6})$

(16) $(15a-18b) \div 3$

(17) $(24x+16y) \div (-8)$

(18) $5(a-2b)+4(2a-b)$

(19) $6(x+y)-2(x+2y)$

(20) $-3(2a+4b-5)+2(3a+6b-1)$

(21) $\frac{1}{4}(8x-4y)+\frac{1}{2}(6x+8y)$

(22) $\frac{1}{8}(x+3y)-\frac{1}{6}(2x+y)$

2. 解き方の手順

各式を丁寧に計算し、同類項をまとめることで式を整理します。

(1) $2x-y+3x-5y = (2x+3x)+(-y-5y) = 5x-6y$

(2) $-3x^2-4x+4x^2+6x = (-3x^2+4x^2)+(-4x+6x) = x^2+2x$

(3) $7a+2b+5-9a+b = (7a-9a)+(2b+b)+5 = -2a+3b+5$

(4) $(3a+2b)+(a-3b) = 3a+2b+a-3b = (3a+a)+(2b-3b) = 4a-b$

(5) $(6x-5y)+(-x+7y) = 6x-5y-x+7y = (6x-x)+(-5y+7y) = 5x+2y$

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

(7) $(4a+3b)-(-2a-b) = 4a+3b+2a+b = (4a+2a)+(3b+b) = 6a+4b$

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

(9) $2a+5b + (4a-5b) = 2a+5b+4a-5b = (2a+4a)+(5b-5b) = 6a$

(10) $(-3x-5y+1)+(x-2y-6) = -3x-5y+1+x-2y-6 = (-3x+x)+(-5y-2y)+(1-6) = -2x-7y-5$

(11) $(8x-3y) - (4x+3y) = 8x-3y-4x-3y = (8x-4x)+(-3y-3y) = 4x-6y$

(12) $(7x-y) - (2x-5y+10) = 7x-y-2x+5y-10 = (7x-2x)+(-y+5y)-10 = 5x+4y-10$

(13) $4(3x-y) = 4 \times 3x - 4 \times y = 12x-4y$

(14) $-6(2a-5b) = -6 \times 2a -6 \times (-5b) = -12a+30b$

(15) $12(\frac{x}{3}+\frac{y}{6}) = 12 \times \frac{x}{3} + 12 \times \frac{y}{6} = 4x+2y$

(16) $(15a-18b) \div 3 = \frac{15a}{3} - \frac{18b}{3} = 5a-6b$

(17) $(24x+16y) \div (-8) = \frac{24x}{-8} + \frac{16y}{-8} = -3x-2y$

(18) $5(a-2b)+4(2a-b) = 5a-10b+8a-4b = (5a+8a)+(-10b-4b) = 13a-14b$

(19) $6(x+y)-2(x+2y) = 6x+6y-2x-4y = (6x-2x)+(6y-4y) = 4x+2y$

(20) $-3(2a+4b-5)+2(3a+6b-1) = -6a-12b+15+6a+12b-2 = (-6a+6a)+(-12b+12b)+(15-2) = 13$

(21) $\frac{1}{4}(8x-4y)+\frac{1}{2}(6x+8y) = 2x-y+3x+4y = (2x+3x)+(-y+4y) = 5x+3y$

(22) $\frac{1}{8}(x+3y)-\frac{1}{6}(2x+y) = \frac{x}{8}+\frac{3y}{8}-\frac{2x}{6}-\frac{y}{6} = \frac{x}{8}+\frac{3y}{8}-\frac{x}{3}-\frac{y}{6} = (\frac{1}{8}-\frac{1}{3})x+(\frac{3}{8}-\frac{1}{6})y = (\frac{3-8}{24})x+(\frac{9-4}{24})y = -\frac{5}{24}x+\frac{5}{24}y$

3. 最終的な答え

(1) $5x-6y$

(2) $x^2+2x$

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

(4) $4a-b$

(5) $5x+2y$

(6) $3x^2+4x+1$

(7) $6a+4b$

(8) $2x+7y$

(9) $6a$

(10) $-2x-7y-5$

(11) $4x-6y$

(12) $5x+4y-10$

(13) $12x-4y$

(14) $-12a+30b$

(15) $4x+2y$

(16) $5a-6b$

(17) $-3x-2y$

(18) $13a-14b$

(19) $4x+2y$

(20) $13$

(21) $5x+3y$

(22) $-\frac{5}{24}x+\frac{5}{24}y$