展开并化简 $2(5m+3n)^2$ 。彻底因式分解 $24(mn)^2 - 21mn^3$ 。

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完整解法

1. Expand the squared binomial using $(a+b)^2=a^2+2ab+b^2$.

$(5m+3n)^2=(5m)^2+2(5m)(3n)+(3n)^2$

$=25m^2+30mn+9n^2$

2. Multiply the expanded expression by 2 and simplify.

$2(5m+3n)^2=2(25m^2+30mn+9n^2)$

$=50m^2+60mn+18n^2$

答案

$50m^2+60mn+18n^2$

1. Rewrite the first term clearly and identify the highest common factor of both terms.

$24(mn)^2-21mn^3=24m^2n^2-21mn^3$

The common factor is $3mn^2$ .

2. Factor out the common factor completely.

$24m^2n^2-21mn^3=3mn^2(8m-7n)$

答案

$3mn^2(8m-7n)$

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