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=x^2(y+9)-y^2(y+9)
=(x^2-y^2)(y+9)
=(x-y)(x+y)(y+9)
học tốt
a) \(9x^2-12x+4\)
\(=9x^2-6x-6x+4\)
\(=3x\left(3x-2\right)-2\left(3x-2\right)\)
\(=\left(3x-2\right)^2\)
b) \(2xy+16-x^2-y^2\)
\(=-\left(x^2-2xy+y^2-16\right)\)
\(=-\left(x-y\right)^2+16\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
c) \(3x+2x^2-2\)
\(=2x^2+4x-x-2\)
\(=2x\left(x+2\right)-\left(x+2\right)=\left(x+2\right)\left(2x-1\right)\)
\(6y^2\left(x-1\right)+9y\left(x-1\right)\)
\(=\left(6y^2+9y\right)\left(x-1\right)=3y\left(2y+3\right)\left(x-1\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
x^3-9x^2+6x+16
=x^3+x^2-10x^2-10x+16x+16
=(x^3+x^2)-(10x^2+10x)+(16x+16)
=x^2(x+1)-10x(x+1)+16(x+1)
=(x+1)(x^2-10x+16)
=(x+1)(x^2-2x-8x+16)
=(x+1)[(x^2-2x)-(8x-16)]
=(x+1)[x(x-2)-8(x-2)]
=(x+1)(x-2)(x-8)
=[( x2)2 +2 x23y + (3y)2 ]-1 =(x2 +3y)2 -12 = (x2+3y-1)(x2+3y+1)
1) \(5x^2-5xy-9x+9y\)
\(=5x\left(x-y\right)-9\left(x-y\right)\)
\(=\left(5x-9\right)\left(x-y\right)\)
2) \(m^3+4m^2+3m\)
\(=m^3+3m^2+m^2+3m\)
\(=m^2.\left(m+3\right)+m\left(m+3\right)\)
\(=\left(m^2+m\right)\left(m+3\right)\)
\(=m\left(m+1\right)\left(m+3\right)\)
3) \(x^2-2xy-15y^2\)
\(=x^2-2xy+y^2-16y^2\)
\(=\left(x-y\right)^2-\left(4y\right)^2\)
\(=\left(x-y-4y\right)\left(x-y+4y\right)\)
\(a,4x^2-12xy+9y^2=\left(2x-3y\right)^2\)
\(b,x^2-9x+20=x^2-4x-5x+20\)
\(=x\left(x-4\right)-5\left(x-4\right)\)
\(=\left(x-4\right)\left(x-5\right)\)
\(c,x^2+7x+12=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)
\(=x^2-y^2-9x-9y=\left(x-y\right)\left(x+y\right)-9\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-9\right)\)