Question

Factories (x+3y)²—x².step by step please ​

Answer 1

opening (x+3y)^2 with identity (a+b)^2

x^2 + 9y^2 + 6xy - x^2

so now

9y^2 +6xy

3y(3y +2x)

Answer 2

Given:

(x+3y)²—x².

To find:

The factorization of a given polynomial.

Solution:

To answer this question, we should know about one of the algebraic identities which is

${a}^{2} - {b}^{2} = (a + b)(a - b) \: \: (i)$

Now,

as given, we have

(x + 3y)² — x²

Considering a = x + 3y and b = x

and comparing with (i)

we get,

(x + 3y)² — x²

= (x + 3y - x) (x + 3y + x)

= (3y) (2x + 3y)

which is a factorised form of (x + 3y)² — x².

Hence,

The factorised form of (x + 3y)² — x² is (3y) (2x + 3y).