How do you multiply ${(3 a - 7 b)}^{2}$ $(3a-7b)^2$ ?

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How do you multiply ${(3 a - 7 b)}^{2}$ $(3a-7b)^2$ ?

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Answer 1 · 2017-01-18T20:45:28

See the entire multiplication process below:

Explanation:

This problem can be rewritten as:

$(3 a - 7 b) (3 a - 7 b)$ $(color(red)(3a) - color(red)(7b))(color(blue)(3a) - color(blue)(7b))$

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$(3 a - 7 b) (3 a - 7 b)$ $(color(red)(3a) - color(red)(7b))(color(blue)(3a) - color(blue)(7b))$ becomes:

$(3 a \times 3 a) - (3 a \times 7 b) - (7 b \times 3 a) + (7 b \times 7 b)$ $(color(red)(3a) xx color(blue)(3a)) - (color(red)(3a) xx color(blue)(7b)) - (color(red)(7b) xx color(blue)(3a)) + (color(red)(7b) xx color(blue)(7b))$

$9 a^{2} - 21 a b - 21 a b + 49 b^{2}$ $9a^2 - 21ab - 21ab + 49b^2$

We can now combine like terms:

$9 a^{2} + (- 21 - 21) a b + 49 b^{2}$ $9a^2 + (-21 - 21)ab + 49b^2$

$9 a^{2} - 42 a b + 49 b^{2}$ $9a^2 - 42ab + 49b^2$

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How do you multiply ${(3 a - 7 b)}^{2}$ $(3a-7b)^2$ ?

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How do you multiply ${(3 a - 7 b)}^{2}$ $(3a-7b)^2$ ?