4x²-y²+4x+1

=(4x²+4x+1)-y²

=(2x+1)²-y²

=(2x+1-y)(2x+1+y)

bài này tớ cũng ko chắc:

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

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

\(1,=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-y-1\right)\left(x+y-1\right)\\ 2,=\left(x+y\right)^3\\ 3,=\left(2y-z\right)\left(4x+7y\right)\\ 4,=\left(x+2\right)^2\\ 5,Sửa:x\left(x-2\right)-x+2=0\\ \Leftrightarrow\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

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

\(4x^2+4x+1-4\)

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

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

\(\left(2x-1\right)\left(2x+3\right)\)

Trả lời:

4x² + 4x - 3

= [ ( 2x )² + 2.2x.1 + 1 ] - 4

= ( 2x + 1 )² - 4

= ( 2x + 1 - 2 ) ( 2x + 1 + 2 )

= ( 2x - 1 ) ( 2x + 3 )

\(4x^2-4x+1=\left(2x\right)^2-2.2x.1+1^2=\left(2x-1\right)^2\\ ---\\ 4x^2-4x-3\\ =4x^2-4x+1-4\\ =\left(2x-1\right)^2-2^2=\left(2x-1-2\right)\left(2x-1+2\right)\\ =\left(2x-3\right)\left(2x+1\right)\)

1: =(2x)^2-2*2x*1+1^2

=(2x-1)^2

2: =4x^2-6x+2x-3

=2x(2x-3)+(2x-3)

=(2x-3)(2x+1)

\(4x^4-8x^3+4x^3-8x^2+x^2-2x-2x+4\\ =4x^3\left(x-2\right)+4x^2\left(x-2\right)+x\left(x-2\right)-2\left(x-2\right)\\ =\left(x-2\right)\left(4x^3+4x^2+x-2\right)\\ =\left(x-2\right)\left(4x^3-2x^2+6x^2-3x+4x-2\right)\\ =\left(x-2\right)\left[2x^2\left(2x-1\right)+3x\left(2x-1\right)+2\left(2x-1\right)\right]\\ =\left(x-2\right)\left(2x-1\right)\left(2x^2+3x-2\right)\)

\(=\left(x^2+x\right)^2+4\left(x^2+x\right)+4-16\\ =\left(x^2+x+2\right)^2-16\\ =\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)\\ =\left(x^2+x-2\right)\left(x^2+x+6\right)\\ =\left(x-1\right)\left(x+2\right)\left(x^2+x+6\right)\)

=\(x^4+2x^3+x^2+4x^2+4x-12\)

=\(x^4+2x^3+5x^2+4x-12\)

=\(x^4-x^3+3x^3-3x^2+8x^2+4x-12\)

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

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

=\(x^3(x-1)+3x^2(x-1)+4[2x(x-1)+3(x-1)]\)

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

=\((x-1)[x^3+3x^2+4(2x+3)]\)

=\((x-1)(x^3+3x^2+8x+12)\)

\(\left(x^2+x\right)^2+\left(4x^2+4x\right)+4-16\\ =\left(x^2+x+2\right)^2-16\\ =\left(x^2+x+2-4\right)\left(x^2+x+2+4\right)\\ =\left(x^2+x-2\right)\left(x^2+x+6\right)\)

4x² - 9y² + 4x - 6y

= (2x - 3y)(2x + 3y) + 2(2x - 3y)

= (2x - 3y)(2x + 3y + 2)

\(4x^2-9y^2+4x-6y\)

\(=\left(4x^2+4x+1\right)-\left(9y^2+6y+1\right)\)

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

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

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