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a)
\(4x^2-9y^2+6x-9y=\left(2x-3y\right)\left(2x+3\right)+3\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+3\right)\)
b)
\(1-2x+2yz+x^2-y^2-z^2=\left(x^2-2x+1\right)-\left(y^2-2yz+z^2\right)\) (đổi dấu)
\(=\left(x-1\right)^2-\left(y-z\right)^2\)
c)
\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5\left(x+1\right)+3\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)
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) 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)
\(x^2+4x-9y^2+4\)
\(=\left(x^2+2.2x+2^2\right)-\left(3y\right)^2\)
\(=\left(x+2\right)^2-\left(3y\right)^2\)
\(=\left(x+2-3y\right)\left(x+2+3y\right)\)
\(x^2-9y^2-6y-1\)
\(=x^2-\left[\left(3y\right)^2+2.3y+1^2\right]\)
\(=x^2-\left(3y+1\right)^2\)
\(=\left(x-3y-1\right)\left(x+3y+1\right)\)
Tham khảo nhé~
a/Ta có:x2+4x-9y2+4
=x2+4x+4-(3y)2
=(x+2)2-(3y)2
=(x+2-3y)(x+2+3y)
b/Ta có:x2-9y2-6xy-1
=x2-6xy-(3y)2-1
=(x-3y-1)(x-3y+1)
a) 3 ( 4x +5y )
b) (x-y) (x+y+1)
d) (x3)2 - 82 = (x3- 8) (x3+8)
a, 12x+15y = 3(4x+5y)
b, x^2 - y^2 - x - y = (x - y)(x + y) - (x + y) = (x + y)(x - y - 1)
c, x^3 + 2x^2 + x = x(x^2 + 2x + 1) = x(x + 1)^2
d, x^6 - 64 = (x^3 - 8)(x^3 + 8) = (x - 2)(x^2 + 2x + 4)(x + 2)(x^2 - 2x + 4)
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^2(y+9)-y^2(y+9)
=(x^2-y^2)(y+9)
=(x-y)(x+y)(y+9)
học tốt
a) 20x2y + 25xy2
= 5xy( 4x + 5y )
b) x2 - 5x - 15y - 9y2
= x(x - 5) - 3y(5 + 3y)