Câu 1:
\(P=2\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2+\left(a+b\right)^2-4b^2=2a^2-2b^2+a^2-2ab+b^2+a^2+2ab+b^2-4b^2=4a^2-4b^2\)
Câu 2:
a) \(=x\left(x-y\right)+7\left(x-y\right)=\left(x-y\right)\left(x+7\right)\)
b) \(=x\left(x^2-6x+9-y^2\right)=x\left[\left(x-3\right)^2-y^2\right]=x\left(x-3-y\right)\left(x-3+y\right)\)
c) \(=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]-15=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15=\left(x^2+5x+4\right)^2+2\left(x^2+5x+4\right)+1-16=\left(x^2+5x+4+1\right)^2-16=\left(x^2+5x+5\right)^2-16=\left(x^2+5x+5-4\right)\left(x^2+5x+5+4\right)=\left(x^2+5x+1\right)\left(x^2+5x+9\right)\)
Câu 3:
\(\left(2x^4+10x^3+x^2+15x-3\right):\left(2x^2+3\right)=\left[x^2\left(2x^2+3\right)+5x\left(2x^2+3\right)-\left(2x^2+3\right)\right]:\left(2x^2+3\right)=\left[\left(2x^2+3\right)\left(x^2+5x-1\right)\right]:\left(2x^2+3\right)=x^2+5x-1\)
