Question

Factorise `4x^2 - 9y^2 + 20x + 25` ?

Answer 1

`(2 x + 5)^2 - 9 y^2`

Explanation:

`4x^2 - 9y^2 + 20x + 25`

`4x^2 + 20x + 25 - 9y^2`

`(2x+5)(2x+5) - 9y^2`

`(2 x + 5)^2 - 9 y^2`

Answer 2

`2x+5-3y)(2x+5+3y)`

Explanation:

`"rearranging the terms"`

`4x^2+20x+25color(blue)(-9y^2)`

`"factorise "4x^2+20x+25`

`(a+-b)^2=a^2+-2ab+b^2larrcolor(blue)"perfect square"`

`4x^2=(2x)^2rArra=2x`

`25=(5)^2rArrb=5`

`2ab=2xx2x xx5=20x`

`rArr4x^2+20x+25=(2x+5)^2`

`rArr4x^2+20x+25color(blue)(-9y^2)`

`=(2x+5)^2-9y^2larrcolor(magenta)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"with "a=2x+5" and "b=3y`

`rArr(2x+5)^2-9y^2`

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