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a) 49( y - 4 )2 - 9( y + 2 )2
= 72( y - 4 )2 - 32( y + 2 )2
= ( 7y - 28 )2 - ( 3y + 6 )2
= ( 7y - 28 - 3y - 6 )( 7y - 28 + 3y + 6 )
= ( 4y - 34 )( 10y - 22 )
= 2( 2y - 17 ).2( 5y - 11 )
= 4( 2y - 17 )( 5y - 11 )
b) 3x2 - 5x - 2 = 3x2 - 6x + x - 2 = 3x( x - 2 ) + ( x - 2 ) = ( x - 2 )( 3x + 1 )
c) x2 - 7xy + 10y2 = x2 - 2xy - 5xy + 10y2 = x( x - 2y ) - 5y( x - 2y ) = ( x - 2y )( x - 5y )
d) 3x2 - 10xy + 3y2 = 3x2 - 9xy - xy + 3y2 = 3x( x - 3y ) - y( x - 3y ) = ( x - 3y )( 3x - y )
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)
\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5\left(x+1\right)+3\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)=\left(x-1\right)\left(x+3\right)^2\)
a) x2 - 6x + 8 = x2 - 2x - 4x + 8 = x(x - 2) - 4(x - 2) = (x - 4)(x - 2)
b) x2 - 5x - 14 = x2 - 7x + 2x - 14 = x(x - 7) + 2(x - 7) = (x + 2)(x - 7)
c) 4x2 - 36x + 56 = 4(x2 - 9x + 14) = 4(x2 - 2x - 7x + 14) = 4[x(x - 2) - 7(x - 2)] = 4(x - 7)(x - 2)
d) 3x2 - 16x + 5 = 3x2 - 15x - x + 5 = 3x(x - 5) - (x - 5) = (3x - 1)(x - 5)
f) 8x2 + 30x + 7 = 8x2 + 16x + 14x + 7 = 8x(x + 2) + 7(x + 2) = (8x + 8)(x + 2)
g) 2x2 - 5xy - 12y2 = 2x2 - 8xy + 3xy - 12y2 = 2x(x - 4y) + 3y(x - 4y) = (2x + 3y)(x - 4y)
h) x2 - 7xy + 10y2 = x2 - 2xy - 5xy + 10y2 = x(x - 2y) - 5y(x - 2y) = (x - 5y)(x - 2y)
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)
Bài 1:tìm x ,biết:
a) (2x - 1)(3x + 2) - 6x(x + 1) = 0
\(\Leftrightarrow6x^2+x-2-6x^2-6x=0\)
\(\Leftrightarrow-5x=2\)
\(\Leftrightarrow x=\frac{-2}{5}\)
b) \(\left(4x-1\right)^2-\left(2x+1\right)\left(8x-3\right)=0\)
\(\Leftrightarrow16x^2-8x+1-16x^2-2x+3=0\)
\(\Leftrightarrow-10x=-4\)
\(\Leftrightarrow x=\frac{2}{5}\)
c) \(4x^2-1=2\left(2x+1\right)\)
\(\Leftrightarrow\left(2x+1\right)\left(2x-1\right)-2\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x+1\right)\left(2x-3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{2}\\x=\frac{3}{2}\end{cases}}\)
2a) \(4x^2-9y^2-6y-1=4x^2-\left(3y+1\right)^2\)
\(=\left(2x-3y-1\right)\left(2x+3y+1\right)\)
b) \(4x^2-1-2x\left(2x-1\right)=\left(2x-1\right)\left(2x+1\right)-2x\left(2x-1\right)\)
\(=1.\left(2x-1\right)\)
c) \(x^2-8x-4y^2+16=\left(x-4\right)^2-4y^2\)
\(=\left(x-4-2y\right)\left(x-4+2y\right)\)
d) \(9x^2-12x-y^2+4=\left(3x-2\right)^2-y^2\)
\(=\left(3x-2-y\right)\left(3x-2+y\right)\)
e) \(4x^2+10x-5=4x^2+2.2.\frac{5}{2}x+\frac{25}{4}-\frac{25}{4}-5\)
\(=\left(2x+\frac{5}{2}\right)^2-\frac{45}{4}\)
\(=\left(2x+\frac{5+3\sqrt{5}}{2}\right)\left(2x+\frac{5-3\sqrt{5}}{2}\right)\)
a) \(x^2+6x+8\)
\(=\left(x^2-2x\right)-4x+8\)
\(=x\left(x-2\right)-4\left(x-2\right)\)
\(\left(x-2\right)\left(x-4\right)\)
b) \(x^2-7xy+10y^2\)
\(=x^2-2xy-5xy+10y^2\)
\(=x\left(x-2y\right)-5y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)
a) x2 - 6x + 8
= x2 -2x - 4x +8
= x( x-2) -4( x-2)
= ( x-2)(x-4)
b1:
câu a,f áp dụng a2-b2=(a-b)(a+b)
câu b,c áp dụng a3-b3=(a-b)(a2+ab+b2)
câu d: \(x^2+2xy+x+2y=x\left(x+2y\right)+\left(x+2y\right)=\left(x+1\right)\left(x+2y\right)\)
câu e: \(7x^2-7xy-5x+5y=7x\left(x-y\right)-5\left(x-y\right)=\left(7x-5\right)\left(x-y\right)\)
câu g xem lại đề
Bài làm
a) 4x2 - 6x
= 2x( 2x - 3 )
b) 9x4y3 + 3x2y4
= 3x2y3( 3x2 + y )
c) x3 - 2x2 + 5x
= x( x2 - 2x + 5 )
d) 3x( x - 1 ) + 5( x - 1 )
= ( x - 1 )( 3x + 5 )
e) 2x2( x + 1 ) + 4( x + 1 )
= ( x + 1 )( 2x2 + 4 )
= ( x + 1 )2( x2 + 2 )
= 2( x + 1 )( x2 + 2 )
f) -3x - 6xy + 9xz
= -( 3x + 6xy - 9xz )
= -3x( 1 + 2y - 3z )
# Học tốt #
a) x4 + 6x2y + 9y2 - 1
= (x2 + 3y)2 - 1
= (x2 + 3y + 1)(x2 + 3y - 1)
b) 2x2 + 3x - 5
= 2x2 - 2x + 5x - 5
= 2x(x - 1) + 5(x - 1)
= (2x + 5)(x - 1)
c) x2 - 7xy + 10y2
= x2 - 2xy - 5xy + 10y2
= x(x - 2y) - 5y(x - 2y)
= (x - 5y)(x - 2y)
a, \(x^4+6x^2y+9y^2-1\)
\(=\left(x^2+3y\right)^2-1\)
\(=\left(x^2+3y-1\right)\left(x^2+3y+1\right)\)
b, \(2x^2+3x-5\)
\(=2x^2-2x+5x-5\)
\(=2x\left(x-1\right)+5\left(x-1\right)=\left(x-1\right)\left(2x+5\right)\)
c, \(x^2-7xy+10y^2\)
\(=x^2-4xy+4y^2-3xy+6y^2\)
\(=\left(x-2y\right)^2-3y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x-5y\right)\)