Question

16（a-b)^2-9(a+b)^2和3(x-y)^3+12(y-x)这两道题怎样因式分解

要有步骤，一步步不要省略，10分悬赏，抢啊！！！！！！！！！！！！！！！！！！！！

Answer 1

16（a-b)^2-9(a+b)^2
=[4(a-b)+3(a+b)]*[4(a-b)-3(a+b)]
=(7a-b)(a-7b)

3(x-y)^3+12(y-x)
=3(x-y)^3-12(x-y)
=3(x-y)[(x-y)^2-4]
=(x-y)(x-y+2)(x-y-2)

Answer 2

16*(a-b)*(a-b)-9*(a+b)*(a+b)
3*(x-y)*(x-y)*(x-y)+12*(y-x)
运算优先级跟数学中的差不多，平方的一定要分开来写就可以了！其它的也没什么！

Answer 3

16(a-b)^2-9(a+b)^2=(7a-b)(a-7b)
注释：x^2-y^2=(x-y)(x+y)
16(a-b)^2=[4(a-b)]^2
9(a+b)^2=[3(a+b)]^2

3(x-y)^3+12(y-x)
=3(x-y)^3-4*[3(x-y)]
=3(x-y)[(x-y)^2-4]
=3(x-y)[(x-y)^2-2^2]
=(x-y)(x-y+2)(x-y-2)