How do you factorise:

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

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

### 3 Answers | Add Yours

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) `

`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)`

`(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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