a, 4x²-49-12xy+9y²

=4x²-12xy+9y²-49

=(2x-3y)²-7²

=(2x-3y-7)(2x-3y+7)

b) \(x^2-7x+10\)

\(=x^2-5x-2x+10\)

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

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

a: \(ab+a+b+1\)

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

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

c: \(4x^2-12xy+3x-9y\)

\(=4x\left(x-3y\right)+3\left(x-3y\right)\)

\(=\left(x-3y\right)\left(4x+3\right)\)

a/25-9y^2-4x^2+12xy

=-(9y^2-12xy+4x^2-25)

=-[(3y)^2-2.3y.2x+(2x)^2-5^2]

=-[(3y-2x)^2-5^2]

=-(3y-2x-5)(3y-2x+5)

b/4x^2-8xy+4y^2-5x+5y

=4(x^2-2.x.y+y^2)-5(x-y)

=4(x-y)^2-5(x-y)

=(x-y)(4x-4y-5)

a: =(2x-3y)^2-4(2x-3y)

=(2x-3y)(2x-3y-4)

b: =3x^2+21x-x-7

=(x+7)(3x-1)

c: =(3x-1)^4+2(3x-1)^2+1

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

d: =2x^3-2x^2-x^2+x+x-1

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

\(-4x^2+12xy-9y^2+25=25-\left(2x-3y\right)^2=\left(5-2x+3y\right)\left(5+2x-3y\right)\)

\(-4x^2+12xy-9y^2+25\)

\(=25-\left(4x^2-12xy+9y^2\right)\)

\(=25-\left(2x-3\right)^2\)

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

\(-4x^2+12xy-9y^2+25\)
\(=\left(-4x^2+12xy-9y^2\right)+25\)
\(=-\left(4x^2-12xy+9y^2\right)+25\)
\(=-\left(2x-3y\right)^2+25\)
Chúc học tốt tick mk nha

a) Ta có: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)

\(=\left(4x^2-3x-18-4x^2-3x\right)\left(4x^2-3x-18+4x^2+3x\right)\)

\(=\left(-6x-18\right)\left(8x^2-18\right)\)

\(=-6\left(x+3\right)\cdot2\left(4x^2-9\right)\)

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

b) Ta có: \(9\left(x+y-1\right)^2-4\left(2x+3y+1\right)^2\)

\(=\left(3x+3y-3\right)^2-\left(4x+6y+2\right)^2\)

\(=\left(3x+3y-3-4x-6y-2\right)\left(3x+3y-3+4x+6y+2\right)\)

\(=-\left(x+3y+5\right)\left(7x+9y-1\right)\)

c) Ta có: \(-4x^2+12xy-9y^2+25\)

\(=-\left(4x^2-12xy+9y^2-25\right)\)

\(=-\left[\left(2x-3y\right)^2-25\right]\)

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

d) Ta có: \(x^2-2xy+y^2-4m^2+4mn-n^2\)

\(=\left(x^2-2xy+y^2\right)-\left(4m^2-4mn+n^2\right)\)

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

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

a) (4x²-3x-18)²-(4x²+3x)²

=(4x²-3x-18-4x²-3x)(4x²-3x-18+4x²+3x)

=(-6x-18)(8x²-18)

=-48x³+108x-144x²+324

a) \(4x^2y^2-12xy+9y^2\)

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

b) \(25x^2-36y^2\)

\(=\left(5x\right)^2-\left(6y\right)^2\)

\(=\left(5x+6y\right)\left(5x-6y\right)\)

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

b)\(\left(2x\right)^2+2×2x+1^2=\left(2x+1\right)^2\)

c)\(\left(2x\right)^2+2×2x×3y+\left(3y\right)^2=\left(2x+3y\right)^2\)

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