Question

factories the polynomial

16x² + 48xy + 36y²​

Answer 1

Answer:

4(2x + 3y)² = 16x² + 48cy + 36y²

Step-by-step explanation:

Given polynomial: 16x² + 48xy + 36y² and we need to factorise it.

→ 16x² + 48xy + 36y²

Take 4 common from it

→ 4(4x² + 12xy + 9y²)

Now, 4x² can be written as (2x)² while 9y² can be written as (3y)². As 2 and 3 are the perfect squares of 4 and 9. So, if we square (2x + 3y) we will get 4x² + 12xy + 9y².

Used identity: (a + b)² = a² + b² + 2ab

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

→ (2x + 3y)² = 4x² + 9y² + 12xy

→ (2x + 3y) = 4x² + 12xy + 9y²

Therefore,

4(2x + 3y)² = 16x² + 48cy + 36y²

Answer 2

$\begin{gathered}\huge\blue{\mid{\fbox{\tt{SOLUTION}}\mid}} \\ \end{gathered}$

Explanation : -

First note that all of the terms are divisible by 4, so separate that out as a factor:

16x2+48xy+36y2=4(4x2+12xy+9y2)

Next note that both 4x2=(2x)2 and 9y2=(3y)2 are perfect squares. So if we square (2x+3) then the resulting first term will be 4x2 and the last term 9y2. How about the middle term?

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

(2x+3)2=4x2+12xy+9y2

So we have a perfect square trinomial.

Putting it all together:

16x2+48xy+36y2=4(2x+3)2