Question

4-12(y-x)+9(x-y)的平方=

x的平方-xy-5x+5y=
ab-5bc-2a的平方+10ac=
x的平方-6xy+9y的平方-4a的平方=
1-4m的平方-9n的平方+12mn=
t的平方-13t+42=
x的平方-8x-33=
不要过程，直接写答案

Answer 1

4-12(y-x)+9(x-y)的平方=(3x-3y+2)^2

x的平方-xy-5x+5y=x(x-y)-5(x-y)=(x-5)(x-y)

ab-5bc-2a的平方+10ac=b(a-5c)-2a(a-5c)=(b-2a)(a-5c)

x的平方-6xy+9y的平方-4a的平方=(x-3y)^2-4a^2=(x-3y+2a)(x-3y-2a)

1-4m的平方-9n的平方+12mn=1-(3n-2m)^2=(1+3n-2m)(1-3n+2m)

t的平方-13t+42=(t-6)(t-7)

x的平方-8x-33=(x-11)(x+3)

Answer 2

4-12(y-x)+9(x-y)^2
=[3(x-y)-2]^2

x^2-xy-5x+5y
=x^2-5x-(xy-5y)
=x(x-5)-y(x-5)
=(x-y)(x-5)

ab-5bc-2a^2+10ac
=ab-2a^2-(5bc-10ac)
=a(b-2a)-5c(b-2a)
=(b-2a)(a-5c)

x^2-6xy+9y^2-4a^2
=(x-3)^2-4a^2
=(x-3-2a)(x-3+2a)

1-4m^2-9n^2+12mn
=1-(2m-3n)^2
=(1-2m+3n)(1+2m-3n)

t^2-13t+42
=(t-7)(t-6)

x^2-8x-33
=(x-11)(x+3)