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

Answer:

See explanation

Step-by-step 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