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School 数学 問題集(ハロ数) 中3 式の計算 解答 ■ |
インターネット上で中学校の数学を勉強できるよ。 |
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丸付けをして、間違えた問題はもう一度やり直したり、解説を理解していこうね。 |
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解答: |
(1) |
(a−b)(x−1) |
(2) (a−b+4)(a−b−5) |
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(3) |
(a−1)(b+1) |
(4) (a+b)(b−c) |
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(5) |
(a+b+1)(a−b−1) |
(6) (a+1)(a+b−2) |
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(7) |
(a+2)(a−b−1) |
(8) (a2+2a+2)(a2−2a+2) |
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(9) |
(a2+a+1)(a2−a+1) |
(10) (a−b)(ab−ac−bc) |
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解説: |
(1) |
ax−bx−a+b |
=(a−b)x−(a−b) |
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=Ax−A =A(x−1) =(a−b)(x−1) | |
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(2) |
a2−2ab+b2−a+b−20 |
=(a−b)2−(a−b)−20 |
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=A2−A−20 =(A+4)(A−5) =(a−b+4)(a−b−5) | |
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(3) |
ab+a−b−1 |
=b(a−1)+(a−1) |
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=bA+A =A(b+1) =(a−1)(b+1) | |
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(4) |
b2+ab−bc−ac |
=b(b−c)+a(b−c) |
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=bA+aA =A(a+b) =(a+b)(b−c) | |
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(5) |
a2−b2−2b−1 |
=a2−(b2+2b+1) |
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=a2−(b+1)2 =A2−B2 =(A+B)(A−B) =(a+b+1)(a−b−1) | |
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(6) |
a2+ab−a+b−2 |
=a2−a−2+ab+b |
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=(a+1)(a−2)+b(a+1) =(a−2)A+bA =A(a−2+b) =(a+1)(a+b−2) | |
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(7) |
a2−ab+a−2b−2 |
=a2+a−2−ab−2b |
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=(a+2)(a−1)−b(a+2) =A(a−1)−bA =A(a−1−b) =(a+2)(a−b−1) | |
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(8) |
a4+4 |
=a4+4a2+4−4a2 |
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=(a2+2)2−(2a)2 =A2−B2 =(A+B)(A−B) =(a2+2a+2)(a2−2a+2) | |
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(9) |
a4+a2+1 |
=a4+2a2+1−a2 |
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=(a2+1)2−a2 =A2−B2 =(A+B)(A−B) =(a2+a+1)(a2−a+1) | |
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(10) |
a2(b−c)+b2(c−a) |
=a2b−a2c+b2c−ab2 |
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=(a2b−ab2)−c(a2−b2) =ab(a−b)−c(a+b)(a−b) =abA−c(a+b)A =A(ab−ac−bc) =(a−b)(ab−ac−bc) | |
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(5点×10問=50点) |
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