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20 tháng 4 2017

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 - 18 = (2x)3 – (12)3 = (2x - 12)[(2x)2 + 2x . 12 + (12)2]

= (2x - 12)(4x2 + x + 14)

d) 125x2 – 64y2 = (15x)2- (8y)2 = (15x + 8y)(15x - 8y)

2 tháng 8 2017

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)

8 tháng 12 2017

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) \(\frac{1}{25}x^2-64y^2\)

\(=\left(\frac{1}{5}x\right)^2-\left(8y\right)^2\)

\(=\left(\frac{1}{5}x-8y\right)\left(\frac{1}{5}x+8y\right)\)

8 tháng 12 2017

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)\(\frac{1}{25}x^2-64y^2=\left(\frac{1}{5}\right)^2-\left(8y\right)^2\)\(=\left(\frac{1}{5}-8y\right)\left(\frac{1}{5}+8y\right)\)

7 tháng 9 2017

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)  \(\frac{1}{25}x^2\)\(-\)\(64y^2\)

=\(\left(\frac{1}{25}x-8y\right)\left(\frac{1}{5}x+8y\right)\)

9 tháng 12 2023

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)

9 tháng 12 2023

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

20 tháng 11 2021

câu b sai r 

\(\dfrac{1}{3}xy+x^2z+xz=3x\left(\dfrac{1}{9}y+\dfrac{1}{3}xz+\dfrac{1}{3}z\right)\)

AH
Akai Haruma
Giáo viên
20 tháng 11 2021

Lời giải:

a.

$=\frac{1}{2}(x^2-4y^2)=\frac{1}{2}[x^2-(2y)^2]=\frac{1}{2}(x-2y)(x+2y)$

b.

$=\frac{1}{3}x(y+3xz+3z)$

c.

$=\frac{2}{25}x(225x^2-4)=\frac{2}{25}(15x-2)(15x+2)$

d.

$=\frac{1}{5}x^2(2+25x+5y)$

\(4x^4+4x^2+1=\left(2x^2+1\right)^2\)

\(9x^4-6x^2+1=\left(3x^2-1\right)^2\)

\(\dfrac{x^2}{9}-\dfrac{2}{3}x+1=\left(\dfrac{x}{3}+1\right)^2\)

\(x^2-25=\left(x-5\right)\left(x+5\right)\)

24 tháng 9 2017

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)

24 tháng 9 2017

\(a,x^2+6x+9=\left(x+3\right)^2\)

Bài giải:

1.

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)

2.

a) x3 + 127 = x3 + (13)3 = (x + 13)(x2 – x . 13+ (13)2)

=(x + 13)(x213x + 19)

b) (a + b)3 – (a - b)3

= [(a + b) – (a – b)][(a + b)2 + (a + b) . (a – b) + (a – b)2]

= (a + b – a + b)(a2 + 2ab + b2 + a2 – b2 + a2 – 2ab + b2)

= 2b . (3a3 + b2)

c) (a + b)3 + (a – b)3 = [(a + b) + (a – b)][(a + b)2 – (a + b)(a – b) + (a – b)2]

= (a + b + a – b)(a2 + 2ab + b2 – a2 +b2 + a2 – 2ab + b2]

= 2a . (a2 + 3b2)

d) 8x3 + 12x2y + 6xy2 + y3 = (2x)3 + 3 . (2x)2 . y +3 . 2x . y + y3 = (2x + y)3

e) - x3 + 9x2 – 27x + 27 = 27 – 27x + 9x2 – x3 = 33 – 3 . 32 . x + 3 . 3 . x2 – x3 = (3 – x)3

19 tháng 11 2021

\(a,=2\left(\dfrac{1}{4}x^2-y^2\right)=2\left(\dfrac{1}{2}x-y\right)\left(\dfrac{1}{2}x+y\right)\\ b,=\dfrac{1}{3}x\left(y+3xz+3z\right)\\ c,=2x\left(9x^2-\dfrac{4}{25}\right)=2x\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)\)

\(d,=x^2\left(\dfrac{2}{5}+5x+y\right)\\ e,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ f,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ g,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)