easy!!!!!

Algebra Level 1

Factorize the expression: 9 x 2 − 6 a x + ( a 2 − b 2 ) 9x^2-6ax +(a^2-b^2)

( 3 x − a − b ) ( 3 x − a − b ) (3x-a-b)(3x-a-b ) ( 3 x − a + b ) ( 3 x − a − b ) (3x-a+b)(3x-a-b ) ( 3 x + a + b ) ( 3 x + a + b ) (3x+a+b)(3x+a+b)

Lakshay Gulati by Lakshay Gulati , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Paola Ramírez
Jan 16, 2015

Let m = a + b m=a+b and n = a − b n=a-b

Then 9 x 2 − 6 a x + m n 9x^2-6ax+mn

( 3 x − m ) ( 3 x − n ) = 9 x 2 − 3 x m − 3 x n + m n (3x-m)(3x-n)=9x^2-3xm-3xn+mn = 9 x 2 − 3 x ( a + b ) − 3 x ( a − b ) + a 2 + b 2 =9x^2-3x(a+b) -3x(a-b)+a^{2}+b^{2} = 9 x 2 − 6 a x + a 2 − b 2 = 9x^2-6ax+a^2-b^2

So 9 x 2 − 6 a x + ( a 2 − b 2 ) = ( 3 x − a − b ) ( 3 x − a + b ) 9x^2-6ax+(a^2-b^2)=\boxed{(3x-a-b)(3x-a+b)}

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Chew-Seong Cheong
Jul 16, 2017

9 x 2 − 6 a x + ( a 2 − b 2 ) = 9 x 2 − 6 a x + a 2 − b 2 = ( 3 x − a ) 2 − b 2 Using the indentity: x 2 − y 2 = ( x + y ) ( x − y ) = ( 3 x − a + b ) ( 3 x − a − b ) \begin{aligned} 9x^2-6ax+(a^2-b^2) & = 9x^2-6ax+a^2-b^2 \\ & = ({\color{#3D99F6}3x-a})^2 - {\color{#D61F06}b}^2 & \small \color{#3D99F6} \text{Using the indentity: } x^2-{\color{#D61F06}y}^2 = (x+{\color{#D61F06}y})(x-{\color{#D61F06}y}) \\ & = \boxed{({\color{#3D99F6}3x-a}+{\color{#D61F06}b})({\color{#3D99F6}3x-a}-{\color{#D61F06}b})} \end{aligned}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...