Question

factorize the following by using identies
1)9x^2 +6xy+y^2​

Answer 1

Answer:

(3x + y)²

Step-by-step explanation:

We know that: (a + b)² = a²  + 2ab + b²

9x²  + 6xy + y²

can be rewritten as:

(3x)²  + 2(3x)(y) + (y)²

Now (3x)²  + 2(3x)(y) + (y)²  matches the identity a²  + 2ab + b²

Therefore:

(3x)²  + 2(3x)(y) + (y)²

= (3x + y)²

Answer: (3x + y)²

Answer 2

$\huge\bf{Answer:-}$

given:-

$(a + b) {}^{2} = a {}^{2} = a {}^{2} + 2ab + b {}^{2}$

$(9x {}^{2} + 6xy + y {}^{2} )$

Also can be written as:-

$(3x) {}^{2} + 2(3x)y + (y) {}^{2}$

So,

$(3x) {}^{2} + 2(3x)y + (y) {}^{2}$

$(3x) {}^{2} + 2(3x)y + (y) {}^{2}$

Therefore,

$= (3x + y) {}^{2}$

Identity used here:-

$= a {}^{2} + 2ab + b {}^{2}$