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How do you factorise: 16-25(a+3)(a+3) (5x-y)(5x-y)-(y-3x)(y-3x)

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parama9000 | TA , Grade 11 | Valedictorian

Posted April 16, 2013 at 9:45 AM via web

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How do you factorise:

16-25(a+3)(a+3)

(5x-y)(5x-y)-(y-3x)(y-3x)

3 Answers | Add Yours

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pramodpandey | College Teacher | Valedictorian

Posted April 16, 2013 at 9:58 AM (Answer #1)

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Given

16-25(a+3)(a+3)     (i)

since we can write

16=4 x 4

25= 5 x 5

Also we know

`x^2-y^2=(x-y)(x+y)`

therefore given question reduces to

`4^2-5^2(a+3)^2` 

`4^2-(5(a+3))^2`

`=4^2-(5a+15)^2`  ,

let x=4 and y=5a+15

`4^2-(5a+15)^2=(4-(5a+15))(4+(5a+15))`

`=(4-5a-15)(4+5a+15)`

`=(-11-5a)(19+5a)`

`(b)`

`(5x-y)(5x-y)-(y-3x)(y-3x)`

`=(5x-y)^2-(y-3x)^2`

`=((5x-y)-(y-3x))((5x-y)+(y-3x))`

`=(5x-y-y+3x)(5x-y+y-3x)`

`=(8x-2y)(2x)`

`=2(4x-y)(2x)`

`=2(2x)(4x-y)`

`=4x(4x-y) `

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oldnick | Valedictorian

Posted April 16, 2013 at 1:21 PM (Answer #2)

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`16-25(a+3)(a+3)=16-25(a+3)^2=`

`=[4+5(a+3)][4-5(a+3)]=`

`=[4+5a+15][4-5a-15]=` `-(19+5a)(5a+11)`

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oldnick | Valedictorian

Posted April 16, 2013 at 1:29 PM (Answer #3)

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`(5x-y)(5x-y)-(y-3x)(y-3x)=`

`=[(5x-y)+(y-3x)][5x-y)-(y-3x)]= `

`=[5x-y+y-3x][5x-y-y+3x]=`

`=4x(4x-y)`

 

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