Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
a) x2-2xy+y2-4
=(x-y)2-4
=(x-y-4)(x-y+4)
b) ab-a-3b+3
=a(b-1)-3(b-1)
=(a-3)(b-1)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)..\)
\(=a^2\left(1-b\right)\left(1+b\right)-b\left(1-b\right)-a\left(1-b\right).\)
\(=\left(a^2+a^2b-b-a\right)\left(1-b\right)\)
\(=\left(ab+a+b\right)\left(a-1\right)\left(1-b\right)\)
\(a^2+b^2-a^2b^2+ab-a-b\)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)\)
\(=a^2\left(1-b\right)\left(1+b\right)-b\left(1-b\right)-a\left(1-b\right)\)
\(=\left(a^2+a^2b-b-a\right)\left(1-b\right)\)
\(=\left(ab+a+b\right)\left(a-1\right)\left(1-b\right)\)
TL:
\(ab\left(a^2+b^2\right)-xy\left(a^2+b^2\right)\)
\(=\left(ab-xy\right)\left(a^2+b^2\right)\)
a) ta có: (ab -1)^2 +(a+b)^2 =(ab)^2 -2ab +1 +a^2 +2ab +b^2 = a^2.(b^2 +1)+(b^2 +1)+(2ab-2ab)=(b^2 +1)(a^2 +1)
b)ta có: x^4 +2.x^3 -4x-4=[(x^2)^2 +2.(x^2).x +x^2 ] -(x^2 +2.2.x +4)=(x^2 +x)^2 -(x+2)^2=(x^2 +x+x+2)(x^2 +x-x-2)=(x^2 +2x+2)(x^2 -2)