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6 tháng 7 2019

a) 16(4x+5)2 - 25(2x+2)2

\(=\left[4\left(4x+5\right)\right]^2-\left[5\left(2x+2\right)\right]^2\)

\(=\left[4\left(4x+5\right)+5\left(2x+2\right)\right]\left[4\left(4x+5\right)-5\left(2x+2\right)\right]\)

\(=\left(16x+20+10x+10\right)\left(16x+20-10x-10\right)\)

\(=\left(26x+30\right)\left(6x+10\right)\)

6 tháng 7 2019

\(b,\left(x-y+4\right)^2-\left(2x+3y-1\right)^2\)

\(=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-2y+1\right)\)

\(=\left(3x+2y+3\right)\left(-x-3y+5\right)\)

\(c,\left(x+1\right)^4-\left(x-1\right)^4\)

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

\(=\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\)

\(=\left(x^2+2x+1+x^2-2x+1\right)\left[\left(x+1+x-1\right)\left(x+1-x+1\right)\right]\)

\(=\left(2x^2+2\right)2x.2\)

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

\(=8x\left(x^2+1\right)\)

15 tháng 7 2018

\(a,36x^2-\left(3x-2\right)^2=\left(6x-3x+2\right)\left(6x+3x-2\right)\)

\(=\left(3x+2\right)\left(9x-2\right)\)

phần b,c,d lm tg tự

\(e,16x^2-24xy+9y^2=\left(4x-3y\right)^2\)

3 tháng 9 2018

\(x^2-2x-4y^2-4y\)

\(=\left(x^2-4y^2\right)-\left(2x+4y\right)\)

\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)

\(=\left(x+2y\right)\left(x-2y-2\right)\)

1 tháng 10 2020

\begin{array}{l} a){\left( {ab - 1} \right)^2} + {\left( {a + b} \right)^2}\\  = {a^2}{b^2} - 2ab + 1 + {a^2} + 2ab + {b^2}\\  = {a^2}{b^2} + 1 + {a^2} + {b^2}\\  = {a^2}\left( {{b^2} + 1} \right) + \left( {{b^2} + 1} \right)\\  = \left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)\\ c){x^3} - 4{x^2} + 12x - 27\\  = {x^3} - 27 + \left( { - 4{x^2} + 12x} \right)\\  = \left( {x - 3} \right)\left( {{x^2} + 3x + 9} \right) - 4x\left( {x - 3} \right)\\  = \left( {x - 3} \right)\left( {{x^2} + 3x + 9 - 4x} \right)\\  = \left( {x - 3} \right)\left( {{x^2} - x + 9} \right)\\ b){x^3} + 2{x^2} + 2x + 1\\  = {x^3} + 2{x^2} + x + x + 1\\  = x\left( {{x^2} + 2x + 1} \right) + \left( {x + 1} \right)\\  = x{\left( {x + 1} \right)^2} + \left( {x + 1} \right)\\  = \left( {x + 1} \right)\left( {x\left( {x + 1} \right) + 1} \right)\\  = \left( {x + 1} \right)\left( {{x^2} + x + 1} \right)\\ d){x^4} - 2{x^3} + 2x - 1\\  = {x^4} - 2{x^3} + {x^2} - {x^2} + 2x - 1\\  = {x^2}\left( {{x^2} - 2x + 1} \right) - \left( {{x^2} - 2x + 1} \right)\\  = \left( {{x^2} - 2x + 1} \right)\left( {{x^2} - 1} \right)\\  = {\left( {x - 1} \right)^2}\left( {x - 1} \right)\left( {x + 1} \right)\\  = {\left( {x - 1} \right)^3}\left( {x + 1} \right)\\ e){x^4} + 2{x^3} + 2{x^2} + 2x + 1\\  = {x^4} + 2{x^3} + {x^2} + {x^2} + 2x + 1\\  = {x^2}\left( {{x^2} + 2x + 1} \right) + \left( {{x^2} + 2x + 1} \right)\\  = \left( {{x^2} + 2x + 1} \right)\left( {{x^2} + 1} \right)\\  = {\left( {x + 1} \right)^2}\left( {{x^2} + 1} \right) \end{array}

19 tháng 9 2018

a ) 36x2 - ( 3x - 2 )2 

= ( 6x - 3x + 2 ) ( 6x + 3x - 2 )

= ( 3x + 2 ) ( 9x - 2 )

b ) 16.( 4x + 5 )2 - 25. ( 2x + 2 )2

= [ 4.( 4x + 5 ) + 5. ( 2x + 2 ) ] [ 4 .( 4x + 5 ) - 5. ( 2x + 2 ) ]

= ( 16x + 5 + 10x + 10 ) ( 16x + 5 - 10x - 10 )
= ( 26x + 15 ) ( 6x - 5 )

a ) 36x2 - ( 3x - 2 )2

= ( 6x - 3x + 2 ) ( 6x + 3x - 2 )

= ( 3x + 2 ) ( 9x - 2 )

b ) 16.( 4x + 5 )2 - 25. ( 2x + 2 )2

= [ 4.( 4x + 5 ) + 5. ( 2x + 2 ) ] [ 4 .( 4x + 5 ) - 5. ( 2x + 2 ) ]

= ( 16x + 5 + 10x + 10 ) ( 16x + 5 - 10x - 10 )

= ( 26x + 15 ) ( 6x - 5 )

25 tháng 9 2016

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

3) \(\frac{x^2}{9}-\frac{y^2}{16}=\left(\frac{x}{3}-\frac{y}{4}\right)\left(\frac{x}{3}+\frac{y}{4}\right)\)

4) \(a^4-b^4=\left(a^2-b^2\right)\left(a^2+b^2\right)=\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)\)

5) \(\left(a-b\right)^2-1=\left(a-b+1\right)\left(a-b-1\right)\)

6) \(4-\left(a-b\right)^2=\left(2-a+b\right)\left(2+a-b\right)\)

7) \(\left(x-y\right)^2-\left(m+n\right)^2=\left(x-y-m-n\right)\left(x-y+m+n\right)\)

8) \(\left(3x-2y\right)^2-\left(2x-3y\right)^2=\left(3x-2y-2x+3y\right)\left(3x-2y+2x-3y\right)\)

\(=\left[3\left(x+y\right)-2\left(x+y\right)\right]\left[3\left(x-y\right)+2\left(x-y\right)\right]=5\left(x+y\right)\left(x-y\right)\)

9) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

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

11) \(\left(a^4+4-4x^2\right)=\left(a^2-2\right)^2\)

16 tháng 10 2018

\(1,4x^4+4x^2y^2-8y^4\)

\(=4\left(x^4+x^2y^2-y^4-y^4\right)\)

\(=4\left[\left(x^4-y^4\right)+\left(x^2y^2-y^4\right)\right]\)

\(=4\left[\left(x^2+y^2\right)\left(x^2-y^2\right)+y^2\left(x^2-y^2\right)\right]\)

\(=4\left(x^2-y^2\right)\left(x^2+y^2+y^2\right)\)

\(=4\left(x-y\right)\left(x+y\right)\left(x^2+2y^2\right)\)

16 tháng 10 2018

\(2,12x^2y-18xy^2-30y^3\)

\(=6y\left(2x^2-3xy-5y^2\right)\)

\(=6y\left[\left(2x^2+2xy\right)-\left(5xy+5y^2\right)\right]\)

\(=6y\left[2x\left(x+y\right)-5y\left(x+y\right)\right]\)

\(=6y\left(x+y\right)\left(2x-5y\right)\)

16 tháng 8 2018

\(\left(x-5\right)^2-16=\left(x-5\right)^2-4^2=\left(x-5-4\right)\left(x-5+4\right)=\left(x-9\right)\left(x-1\right)\)

\(25-\left(3-x\right)^2=5^2-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)

\(\left(7x-4\right)^2-\left(2x+1\right)^2=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)=\left(5x-5\right)\left(9x-3\right)=15\left(x-1\right)\left(3x-1\right)\)\(49\left(y-4\right)^2-9\left(y+2\right)^2=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2=\left(7y-28-3y-6\right)\left(7y-28+3y-6\right)=\left(4y-34\right)\left(10y-22\right)\)\(=4.\left(2y-17\right)\left(5y-11\right)\)

e); f) Áp dụng hằng đẳng thức số 6,7 để làm

27 tháng 10 2017

a) \(=2xy^2\left(x^2+8x+15\right)\)

\(=2xy^2\left[\left(x^2+8x+16\right)-1\right]\)

\(=2xy^2\left[\left(x+4\right)^2-1\right]\)

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

\(=2xy^2\left(x+5\right)\left(x-3\right)\)

mấy câu sau tự làm nha :*

29 tháng 10 2017

b,=(x^2-10x+25)-4

  =(x-5)^2-2^2

  =(x-5-2)(x-5+2)

  =(x-7)(x-3)