化简 $-4(2a + b) + 7(b - 3a)$ 。因式分解 $12xy + 6x^2 - 2y - x$ 。

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完整解法

1. Expand both brackets carefully, including the negative coefficient.

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

$= -8a-4b+7b-21a$

2. Collect like terms and simplify the expression.

$-8a-21a-4b+7b$

$= -29a+3b$

答案

$-29a+3b$

1. Group the four terms so that each pair has a common factor.

$12xy+6x^2-2y-x$

$= (12xy+6x^2) + (-2y-x)$

2. Factorise each group to reveal a common bracket.

$(12xy+6x^2)+(-2y-x)$

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

3. Factor out the common binomial factor completely.

$6x(2y+x)-1(2y+x)$

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

答案

$(2y+x)(6x-1)$

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