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

asked Sep 18, 2020 52.6k views

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1 vote

Answer:

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

Ken Fox answered Sep 25, 2020

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