Question

Factor. ​9x^2+42xy+49y^2​ Enter your answer in the box

Answer 1

$\qquad \qquad\huge \underline{\boxed{\sf ᴀɴsweʀ}}$

The factorized form of the given equation is ~

$\boxed{ \sf(3x + 7y) {}^{2} }$

Let's solve ~

$\qquad \sf \dashrightarrow \: 9 {x}^{2} + 42xy + 49 {y}^{2}$

$\qquad \sf \dashrightarrow \: (3x) {}^{2} + 2(3x \times 7y) + (7y) {}^{2}$

Now, as we can see, an Identity is applied here ~

that is ;

$\qquad \sf \dashrightarrow \: {a}^{2} + 2ab + {b }^{2} = (a + b) {}^{2}$

So, let's use this identity in our next step, taking :

• a = 3x

• b = 7y

$\qquad \sf \dashrightarrow \: (3x + 7y) {}^{2}$