Question

Factor. ​9x^2+42xy+49y^2​
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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 * 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)`