How do you multiply ${(2 b + 5 a)}^{2}$ $(2b+5a)^2$ ?

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Answer 1 · 2016-12-21T04:53:34

$4 b^{2} + 20 a b + 25 a^{2}$ $4b^2 + 20ab + 25a^2$

We can expand this expression as:

${(2 b + 5 a)}^{2} \to (2 b + 5 a) (2 b + 5 a)$ $(2b + 5a)^2 -> (2b + 5a)(2b + 5a)$

Now we can cross multiple the terms in each set of parenthesis:

$(2 b + 5 a) (2 b + 5 a) \to$ $(2b + 5a)(2b + 5a) ->$

$(2 b \cdot 2 b) + (2 b \cdot 5 a) + (5 a \cdot 2 b) + (5 a \cdot 5 a) \to$ $(2b*2b) + (2b*5a) + (5a*2b) + (5a*5a) ->$

$4 b^{2} + 10 a b + 10 a b + 25 a^{2}$ $4b^2 + 10ab + 10ab + 25a^2$

Next we can add like terms:

$4 b^{2} + (10 + 10) a b + 25 a^{2}$ $4b^2 + (10 + 10)ab + 25a^2$

$4 b^{2} + 20 a b + 25 a^{2}$ $4b^2 + 20ab + 25a^2$

How do you multiply (2b+5a)2(2b+5a)^2?