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a) \(x^2+6x+9\)
\(=\left(x+3\right)^2\)
\(=\left(x+3\right)\left(x+3\right)\)
b) \(10x-25-x^2\)
\(=-\left(x^2-10x+25\right)\)
\(=-\left(x-5\right)^2\)
\(=-\left(x-5\right)\left(x-5\right)\)
c) \(8x^3-\frac{1}{8}\)
\(=\left(2x\right)^3-\left(\frac{1}{2}\right)^3\)
\(=\left(2x-\frac{1}{2}\right)\left(4x^2+x+\frac{1}{4}\right)\)
d) \(\frac{1}{25}x^2-64y^2\)
\(=\left(\frac{1}{5}x\right)^2-\left(8y\right)^2\)
\(=\left(\frac{1}{5}x-8y\right)\left(\frac{1}{5}x+8y\right)\)
a) \(x^2+6x+9=x^2+2.3.x+3^2\)\(=\left(x+3\right)^2\)
b)\(10x-25-x^2=-\left(x^2-10x+25\right)\)\(=-\left(x^2-2.5.x+5^2\right)=-\left(x+5\right)^2\)
c)\(8x^3-\frac{1}{8}=\left(2x\right)^3-\left(\frac{1}{2}\right)^3\)\(=\left(2x-\frac{1}{2}\right)\left(4x+x+\frac{1}{4}\right)\)
d)\(\frac{1}{25}x^2-64y^2=\left(\frac{1}{5}\right)^2-\left(8y\right)^2\)\(=\left(\frac{1}{5}-8y\right)\left(\frac{1}{5}+8y\right)\)
1) -25x6 - y8 + 10x3y4 = -( 25x6 - 10x3y4 + y8 ) = -[ ( 5x3 )2 - 2.5x3.y4 + ( y4 ) ] = -( 5x3 - y4 )2
2) 2x( 3x - 5 ) + 10 - 6x = 2x( 3x - 5 ) - 2( 3x - 5 ) = ( 3x - 5 )( 2x - 2 ) = 2( 3x - 5 )( x - 1 )
3) x2 - 9 - x2( x2 - 9 ) = ( x2 - 9 ) - x2( x2 - 9 ) = ( x2 - 9 )( 1 - x2 ) = ( x - 3 )( x + 3 )( 1 - x )( 1 + x )
4) 4x2 - 9 - ( 3x + 1 )( 2x - 3 ) = ( 2x - 3 )( 2x + 3 ) - ( 3x + 1 )( 2x - 3 )
= ( 2x - 3 )[ ( 2x + 3 ) - ( 3x + 1 ) ]
= ( 2x - 3 )( 2x + 3 - 3x - 1 )
= ( 2x - 3 )( 2 - x )
5) 8x3 - y3 - 4x + 2y = ( 8x3 - y3 ) - ( 4x - 2y )
= [ ( 2x )3 - y3 ) - 2( 2x - y )
= ( 2x - y )( 4x2 + 2xy + y2 ) - 2( 2x - y )
= ( 2x - y )( 4x2 + 2xy + y2 - 2 )
Bài 3
a) x² + 10x + 25
= x² + 2.x.5 + 5²
= (x + 5)²
b) 8x - 16 - x²
= -(x² - 8x + 16)
= -(x² - 2.x.4 + 4²)
= -(x - 4)²
c) x³ + 3x² + 3x + 1
= x³ + 3.x².1 + 3.x.1² + 1³
= (x + 1)³
d) (x + y)² - 9x²
= (x + y)² - (3x)²
= (x + y - 3x)(x + y + 3x)
= (y - 2x)(4x + y)
e) (x + 5)² - (2x - 1)²
= (x + 5 - 2x + 1)(x + 5 + 2x - 1)
= (6 - x)(3x + 4)
Bài 4
a) x² - 9 = 0
x² = 9
x = 3 hoặc x = -3
b) (x - 4)² - 36 = 0
(x - 4 - 6)(x - 4 + 6) = 0
(x - 10)(x + 2) = 0
x - 10 = 0 hoặc x + 2 = 0
*) x - 10 = 0
x = 10
*) x + 2 = 0
x = -2
Vậy x = -2; x = 10
c) x² - 10x = -25
x² - 10x + 25 = 0
(x - 5)² = 0
x - 5 = 0
x = 5
d) x² + 5x + 6 = 0
x² + 2x + 3x + 6 = 0
(x² + 2x) + (3x + 6) = 0
x(x + 2) + 3(x + 2) = 0
(x + 2)(x + 3) = 0
x + 2 = 0 hoặc x + 3 = 0
*) x + 2 = 0
x = -2
*) x + 3 = 0
x = -3
Vậy x = -3; x = -2
Bài giải:
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 - 1818 = (2x)3 – (1212)3 = (2x - 1212)[(2x)2 + 2x . 1212 + (1212)2]
= (2x - 1212)(4x2 + x + 1414)
d) 125125x2 – 64y2 = (15x)2(15x)2- (8y)2 = (1515x + 8y)(1515x - 8y)
a) x2 + 6x + 9 = x2 + 2.3x + 32 = (x + 3)2
b) 10x – 25 – x2 = -(x2 -10x + 25) = -(x2 -2.5x + 52)
= -(x – 5)2
c) 8x3 – 1/8= (2x)3 – ( 1/2)3 = (2x – 1/2)[(2x)2 + 2x . 1/2+ (1/2)2]
= (2x – 1/2)(4x2 + x + 1/4)
d) 1/25x2 – 64y2 = (1/5 x)2– (8y)2 = ( 1/5 x + 8y)(1/5x- 8y)
a) x2 + 6x + 9 = x2 + 2.3.x + 32 = (x + 3)2
b) 10x - 25 - x2 = - (x2 - 2.5.x + 52) = - (x - 5)2
c) \(8x^3-\dfrac{1}{8}=\left(2x\right)^3-\left(\dfrac{1}{2}\right)^3=\left(2x-\dfrac{1}{2}\right)\left(4x^2+x+\dfrac{1}{4}\right)\)
d) 25x2 - 64y2 = (5x)2 - (8y)2 = (5x - 8y)(5x + 8y)
đề dài nên T giải câu a thôi bn tự làm tiếp mấy câu khác nhé
2x^2 - 2y^2 - 6x - 6y
= 2(x^2-y^2) - 6(x+ y)
= 2(x-y)(x+y) - 6(x+y)
= (2(x-y)-6) (x+y)
mình chỉ phân tích thôi
a) 6x(4-x)+x-4
=6x(4-x)-(4-x)
=(6x-1)(4-x)
c) 25x^2-10x+1-16z^2
=(5x-1)^2-16z^2
=(5x-1-4z)(5x-1+4z)
ban xem lại đề bài câu b đi chắc là sai đó
còn các câu trên bạn tự làm nhé
Thực hiện phép tính:
a) (2x-3y)(4x2+6xy+9y2)
=8x3-27y3
b) (6x3+3x2+4x+2):(3x2+2)
=(3x2+2)(2x+1):(3x2+2)
=2x+1
c) (x+2)2+(3-x)-2(x+3)(x-3)
=x2+4x+4+3-x-2x2+18
=-x2+4x+25
a) \(x^2\)\(+\)\(6x\)\(+\)\(9\)
\(=\left(x+3\right)^2\)
b) \(x^3\)\(+\)\(3x^2\)\(+\)\(3x\)\(+\)\(1\)
\(=\left(x+1\right)^3\)
c) \(8x^3\)\(-\)\(\frac{1}{8}\)
\(=\left(2x-\frac{1}{2}\right)\left(4x^2+x+\frac{1}{4}\right)\)
d) \(10x\)\(-\)\(25\)\(-\)\(x^2\)
\(=\)\(-x^2\)\(+\)\(10\)\(-\)\(25\)
\(=-\left(x^2-10+25\right)\)
\(=-\left(x-5\right)^2\)
e) \(\frac{1}{25}x^2\)\(-\)\(64y^2\)
=\(\left(\frac{1}{25}x-8y\right)\left(\frac{1}{5}x+8y\right)\)