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mr Goodwill [35]
2 years ago
5

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

Mathematics
1 answer:
Sonbull [250]2 years ago
6 0

\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}

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