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

`x^2 - 3x - 4`

`<=> x(x - 3)-4`

\(x^2-11x+3\\ =\left(x^2-4x+4\right)-7x-1\\ =\left(x-2\right)^2-\left(\sqrt{7x+1}\right)^2\\ =\left(x-2-\sqrt{7x+1}\right)\left(x-2+\sqrt{7x+1}\right)\)

PHU HUYNH

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

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

\(=\left[\left(x-y\right)^2-1^2\right]+\left(3x-3y-3\right)\)

\(=\left[\left(x-y\right)-1\right]\left[\left(x-y\right)+1\right]+3\left(x-y-1\right)\)

\(=\left(x-y-1\right)\left(x-y+1\right)+3\left(x-y-1\right)\)

\(=\left(x-y-1\right)\left[\left(x-y+1\right)+3\right]\)

\(=\left(x-y-1\right)\left(x-y+4\right)\)

x²-x-y²-y=(x²-y²)-(x+y)=(x-y)(x+y)-(x+y)=(x+y)(x-y-1)

x²-xy+x-y=x(x-y)+(x-y)=(x+1)(x-y)

\(\left(x-2y\right)\left(x+2y\right)+\left(x+1\right)\)

1. (x-3)²

2. (3y+2x)²

3. (1/5x-8y)(1/5x+8y)

4. (x-2y)(x²+2xy+4y²)

5. (4x-3-x-1)(4x-3+x+1)

(3x-4)(5x-2)

\(=x^2+x-6x+6\\ =x\left(x+1\right)-6\left(x+1\right)\\ =\left(x+1\right)\left(x+6\right)\)

\(x^2-6x+7=x^2-6x+9-2\\ =\left(x-3\right)^2-2=\left(x-3-\sqrt{2}\right)\left(x-3+\sqrt{2}\right)\\ x^4+64=x^4+16x^2+64-16x^2\\ =\left(x^2+8\right)^2-16x^2=\left(x^2-4x+8\right)\left(x^2+4x+8\right)\\ a^4+4b^4=a^4+4a^2b^2+4b^4-4a^2b^2\\ =\left(a^2+2b^2\right)^2-4a^2b^2\\ =\left(a^2-2ab+2b^2\right)\left(a^2+2ab+2b^2\right)\)

= x² -7x -x +7

= x. (x-7) - (x-7)

= (x-1)(x-7)

Chúc bạn học tốt nha!