Question

16 x^4 - 45 x^2 y^2 + 81 y^4

Answer 1

First you have to express the highest powers of x and y as squares.

16x^4 = (4x^2)^2 and 81y^4 = (9y^2)^2. Then try squaring

(4x^2 + 9y^2)^2 = 16x^4 + 81y^4 + 2 * 4x^2 * 9y^2 = 16x^4 + 81y^4 + 72 x^2y^2.

The first two terms are OK (by our construction) but the last term is too big. You have to subtract 36x^2y^2 to get the original expression. So the best you can do is

(4x^2 + 9y^2)^2 - 36x^2y^2. This can also be written as

(4x^2 + 9y^2 - 6xy) * (4x^2 + 9y^2 + 6xy).

You can complete the squares in each of the terms in parentheses. Please do it yourself.

please mark as brainliest

Answer 2

❥16x^4-72x^2y^2+81y^4

❥(4x^2-9y^2)^2. by (a-b)^2=a^2+b^2-2ab

❥{(2x+3y)(2x-3y)}^2. by (a+b)(a-b)=a^2-b^2