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(ab-1)2 + (a+b)2
=a2b2-2ab+1+a2+2ab+b2
=a2b2+a2+b2+1
=a2(b2+1)+(b2+1)
=(a2+1)(b2+1)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)..\)
\(=a^2\left(1-b\right)\left(1+b\right)-b\left(1-b\right)-a\left(1-b\right).\)
\(=\left(a^2+a^2b-b-a\right)\left(1-b\right)\)
\(=\left(ab+a+b\right)\left(a-1\right)\left(1-b\right)\)
\(a^2+b^2-a^2b^2+ab-a-b\)
\(=a^2\left(1-b^2\right)+b\left(b-1\right)+a\left(b-1\right)\)
\(=a^2\left(1-b\right)\left(1+b\right)-b\left(1-b\right)-a\left(1-b\right)\)
\(=\left(a^2+a^2b-b-a\right)\left(1-b\right)\)
\(=\left(ab+a+b\right)\left(a-1\right)\left(1-b\right)\)
1, \(a^2b-2ab^2+ab\) = \(ab\left(a-2b+1\right)\)
2, \(a\left(x-1\right)+b\left(1-x\right)\)=\(a\left(x-1\right)-b\left(x-1\right)\)
=\(\left(x-1\right)\left(a-b\right)\)
TL:
\(ab\left(a^2+b^2\right)-xy\left(a^2+b^2\right)\)
\(=\left(ab-xy\right)\left(a^2+b^2\right)\)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
Bạn thấy ảnh ko ạ ?
* Nguồn : Lazi *
Trả lời:
\(\left(ab-1\right)^2+\left(a+b\right)^2\)
\(=a^2b^2-2ab+1+a^2+2ab+b^2\)
\(=a^2b^2+1+a^2+b^2\)
\(=\left(a^2b^2+a^2\right)+\left(b^2+1\right)\)
\(=a^2\left(b^2+1\right)+\left(b^2+1\right)\)
\(=\left(b^2+1\right)\left(a^1+1\right)\)