\(\left(a^2+b^2\right)\left(c^2+d^2\right)=\left(ac+bd\right)^2+\left(ad-bc\right)^2\)

\(\Leftrightarrow a^2c^2+a^2d^2+b^2c^2+b^2c^2+b^2d^2-ac^2-2abcd-b^2d^2-a^2d^2+2abcd-b^2c^2=0\)

=>dpcm

><

=\(\left(x^2-2x+3\right)\left(x^2-4x+1\right)\)

2) \(1-9x^2=\left(1-3x\right)\left(1+3x\right)\)

3) \(\frac{x^2}{9}-\frac{y^2}{16}=\left(\frac{x}{3}-\frac{y}{4}\right)\left(\frac{x}{3}+\frac{y}{4}\right)\)

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

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

6) \(4-\left(a-b\right)^2=\left(2-a+b\right)\left(2+a-b\right)\)

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

8) \(\left(3x-2y\right)^2-\left(2x-3y\right)^2=\left(3x-2y-2x+3y\right)\left(3x-2y+2x-3y\right)\)

\(=\left[3\left(x+y\right)-2\left(x+y\right)\right]\left[3\left(x-y\right)+2\left(x-y\right)\right]=5\left(x+y\right)\left(x-y\right)\)

9) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

10) \(\left(x^4+2x^2+1\right)=\left(x^2+1\right)^2\)

11) \(\left(a^4+4-4x^2\right)=\left(a^2-2\right)^2\)

Đề sai òi