Question

Answer 1

a)

\(x^2-y^2-2x-2y\\ =\left(x^2-y^2\right)-2\left(x+y\right)\\ =\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\\ =\left(x+y\right)\left(x-y-2\right)\)

b)

\(a^2-9-8ab+16b^2\)

\(=\left(a^2-8ab+16b^2\right)-3^2\)

\(=\left(a-4b\right)^2-3^2\\ =\left(a-4b-3\right)\left(a-4b+3\right)\)

Answer 2

\(a,x^2-y^2-2x-2y=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\\ =\left(x-y-2\right)\left(x+y\right)\)

\(b,a^2-9-8ab+16b^2\\ =\left(a^2-8ab+16b^2\right)-3^2\\ =\left(a^2-2.4b.a+\left(4b\right)^2\right)-3^2\\ =\left(a-4b\right)^2-3^2\\ =\left(a-4b-3\right)\left(a-4b+3\right)\)

Áp dụng HĐT : \(a^2-b^2=\left(a-b\right)\left(a+b\right)\\ \left(a-b\right)^2=a^2-2ab+b^2\)

Answer 3

\(a,x^2-y^2-2x-2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-2\right)\)
______________________________
\(b,a^2-9-8ab+16b^2\)
\(=\left(a^2-8ab+16b^2\right)-9\)
\(=\left(a-4b\right)^2-3^2\)
\(=\left(a-4b-3\right)\left(a-4b+3\right)\)

Answer 4

a) =(x-y)(x+y)-(2x+2y) = (x-y)(x+y)-2(x+y) = (x+y)(x-y-2)

 

b) =[a^2- 2.a.4b+ (4b)^2]- 9 = (a-b)^2 - 9 = (a-b)^2- 3^2 = (a-b+3)(a-b-3)