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

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

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

=(a+b+c)(a+b-c)(a-b+c)(a-b-c)

êffeeffe

a/ \(4x^2-49=\left(2x\right)^2-7^2=\left(2x-7\right)\left(2x+7\right)\)

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

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

\(a^6+a^4+a^2b^2+b^4-b^6\)

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

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

\(=(a^2-b^2+1)(a^4+a^2b^2+b^4)\)

\(=(a^4+2a^2b^2+b^4-a^2b^2)(a^2-b^2+1)\)

\(=(a^2+ab+b^2)(a^2-ab+b^2)(a^2-b^2+1)\)

\(a^6+a^2b^2+a^4+b^2-b^6\)

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

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

Ta có

a,    x²-x-y²-y

=x²-y²-(x+y)

=(x-y)(x+y) - (x+y)

=(x+y)(x-y-1)

b,   x²-2xy+y²-z²

=(x-y)²-z²

=(x-y-z)(x-y+z)

con bai 32, 33 neu ban tra loi duoc minh h them

nhanh nha

\(4x^4+4x^3-x^2-x\)

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

\(=\left(x^2+x\right)^2+3\left(x^2+x\right)+2-12\)

\(=\left(x^2+x\right)^2+3\left(x^2+x\right)-10\)

\(=\left(x^2+x+5\right)\left(x^2+x-2\right)\)

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

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