Question

Can someone please explain to me HOW to transform this equation to determine if its an identity (8x+12y)^2+(6x+9y)=(10x+15y)^2

Answer 1

See explanation

Explanation:

Given

`(8x+12y)^2+(6x+9y)^2=(10x+15y)^2`

Note

`(8x+12y)^2=(4(2x+3y))^2=16(2x+3y)^2\\ \\(6x+9y)^2=(3(2x+3y))^2=9(2x+3y)^2\\ \\(10x+15y)^2=(5(2x+3y))^2=25(2x+3y)^2`

Since

`16(2x+3y)^2+9(2x+3y)^2=(2x+3y)^2(16+9)=25(2x+3y)^2,`

this is an identity