因式分解1.a^2-b^2-4bc-4c^22.169(a-b)^2-196(a+b)^23.4a^2-12ab+9b^2-254.x^2(x+1)-y(xy+x)

Question

因式分解
1.a^2-b^2-4bc-4c^2
2.169(a-b)^2-196(a+b)^2
3.4a^2-12ab+9b^2-25
4.x^2(x+1)-y(xy+x)

Answer 1

1）a²-b²-4bc-4c²
=a²-(b²+4bc+4c²)
=a²-(b+2c)²
=(a+b+2c)(a-b-2c)
2）169(a-b)²-196(a+b)²
=[13(a-b)]²-[14(a+b)]²
=(13a-13b+14a+14b)(13a-13b-14a-14b)
=-(27a+b)(a+27b)
3）4a²-12ab+9b²-25
=(2a-3b)²-5²
=(2a-3b+5)(2a-3b-5)
4）x²(x+1)-y(xy+x)
=x³+x²-xy²-xy
=x(x²+x-y²-y)
=x[(x+y)(x-y)+(x-y)]
=x(x-y)(x+y+1)