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Factor. ​9x^2+42xy+49y^2​
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Sagot :

DᴀʀᴋPᴀʀᴀᴅᴏx

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The factorized form of the given equation is ~

[tex] \boxed{ \sf(3x + 7y) {}^{2} }[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: 9 {x}^{2} + 42xy + 49 {y}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (3x) {}^{2} + 2(3x \times 7y) + (7y) {}^{2} [/tex]

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

that is ;

[tex]\qquad \sf  \dashrightarrow \: {a}^{2} + 2ab + {b }^{2} = (a + b) {}^{2} [/tex]

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

  • a = 3x

  • b = 7y

[tex]\qquad \sf  \dashrightarrow \: (3x + 7y) {}^{2} [/tex]

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