Question

Factorise the following :- show the formula
i) 9x² - 4y²
(ii) 20y²x - 45x³ ​

Answer 1

Answer:

The factorization of (i) $9x^{2} - 4y^{2}$ is (3x + 2y) (3x - 2y) (ii) 20$y^{2} x -45x^{3}$ is 5x (2y + 3x)(2y - 3x)

Step-by-step explanation:

(i) 9$x^{2}$ -4 $y^{2}$ = $(3x)^{2}$ - $(2y)^{2}$

Now this is in the form of $a^{2} - b^{2}$,and we know that, $a ^{2} - b^{2} =$ (a +b) ( a - b)

So we can write it as,

$(3x0^{2} - (2 y)^{2}$= (3x + 2y) ( 3x - 2y)

( ii) 20$y^{2} x$ - 45 $x^{3}$

Factors of 20 is 5and 4 and factor of 45 is 5 and 9

20 $y^{2}$x - 45 $x^{3}$ = 5× 4 $y^{2} x$ - 5 ×9 $x^{2}$ × x

                       = 5 x (4 $y^{2}$ - 9 $x^{2}$ )

                       = 5x { $(2y)^{2}$ - $(3x)^{2}$}                   (formula used, $a^{2} - b^{2}$  = (a+ b)(a - b)

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