How do you multiply ${(4 a + b)}^{2}$ $(4a+b)^2$ ?

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How do you multiply ${(4 a + b)}^{2}$ $(4a+b)^2$ ?

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Answer 1 · 2016-09-05T07:32:44

$16 a^{2} + 8 a b + b^{2}$ $16a^2+8ab+b^2$

Explanation:

We can express ${(4 a + b)}^{2}$ $(4a+b)^2$ as $(4 a + b) (4 a + b)$ $(4a+b)(4a+b)$

We must ensure that each term in the 2nd bracket is multiplied by each term in the 1st bracket.

This may be done as follows.

$(4 a + b) (4 a + b) = 4 a (4 a + b) + b (4 a + b)$ $(color(red)(4a+b))(4a+b)=color(red)(4a)(4a+b)color(red)(+b)(4a+b)$

distribute the brackets.

$\Rightarrow 16 a^{2} + 4 a b + 4 a b + b^{2}$ $rArr16a^2+4ab+4ab+b^2$

collecting like terms gives $16 a^{2} + 8 a b + b^{2}$ $16a^2+8ab+b^2$

$\Rightarrow {(4 a + b)}^{2} = 16 a^{2} + 8 a b + b^{2}$ $rArr(4a+b)^2=16a^2+8ab+b^2$

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How do you multiply ${(4 a + b)}^{2}$ $(4a+b)^2$ ?

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Explanation:

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How do you multiply ${(4 a + b)}^{2}$ $(4a+b)^2$ ?