Question

Viết các biểu thức sau dưới dạng tích:

\(a.(x+y+x)^2-(y+z)^2\)

\(b.(x-3)^2-2(x^2-9)+(x+3)^2 \)

\( c.(a^2-b^2)^2-(a+b^2)^2\)

Answer 1

a: \(\left(x+y+z\right)^2-\left(y+z\right)^2\)

\(=\left(x+y+z-y-z\right)\left(x+y+z+y+z\right)\)

\(=x\left(x+2y+2z\right)\)

b: \(\left(x-3\right)^2-2\left(x^2-9\right)+\left(x+3\right)^2\)

\(=\left(x-3-x-3\right)^2\)

=36

Answer 2

c: \(\left(a^2-b^2\right)^2-\left(a+b^2\right)^2\)

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

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

\(=a\cdot\left(a+1\right)\left(a^2-a-2b^2\right)\)