Question

6. 49x^4 + 168x^2y^ 2 + 144y4

Answer 1

step 1 ((49•(x4))-((168•(x2))•(y2)))+(24•32y4)

STEP 2 ((49 • (x4)) - ((23•3•7x2) • y2)) + (24•32y4)

STEP 3 (72x4 - (23•3•7x2y2)) + (24•32y4)

STEP 4 Trying to factor a multi variable polynomial .

4.1 Factoring 49x4 168x2y2+144y4 .

Try to factor this multi-variable trinomial using trial and error Found a factorization : (7x2 - 12y2)•(7x2 - 12y2)

I think his answer wil help you.

Answer 2

Step-by-step explanation:

Given expression is

49x⁴+168x²y²+144y⁴

It can be written as

7²(x²)²+2(7x²)(12y²)+12²(y²)²

=>(7x²)²+2(7x²)(12y²)+(12y²)²

This is in the form of a²+2ab+b²

Here a=7x²; b=12y²

we know that

a²+2ab+b²=(a+b)²=(a+b)(a+b)

=>(7x²)²+2(7x²)(12y²)+(12y²)²

=>(7x²+12y²)²

=>(7x²+12y²)(7x²+12y²)

49x⁴+168x²y²+144y⁴ =

(7x²+12y²)(7x²+12y²)