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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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