How do you multiply $(9 a + 2) (9 a^{2} + a + 1)$ $(9a +2) (9a^2 + a + 1)$ ?

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How do you multiply $(9 a + 2) (9 a^{2} + a + 1)$ $(9a +2) (9a^2 + a + 1)$ ?

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Answer 1 · 2015-08-23T11:01:43

$= 81 a^{3} + 27 a^{2} + 11 a + 2$ $=color(blue)(81a^3 + 27a^2 +11a+2$

Explanation:

$(9 a + 2) (9 a^{2} + a + 1)$ $color(blue)((9a+2))(9a^2+a+1)$
$= (9 a) \cdot (9 a^{2} + a + 1) + (2) . (9 a^{2} + a + 1)$ $=color(blue)((9a)) *(9a^2+a+1) +color(blue)((2)) . (9a^2+a+1)$

note : $a^{m} \cdot a^{n} = a^{m + n}$ $color(blue)(a^m*a^n=a^(m+n)$ , is the property applied to exponents of $a$ $a$

$= 81 a^{3} + 9 a^{2} + 9 a + 18 a^{2} + 2 a + 2$ $=81a^3 +9a^2 +9a + 18a^2 +2a +2$

Adding like terms

$= 81 a^{3} + 27 a^{2} + 11 a + 2$ $=color(blue)(81a^3 + 27a^2 +11a+2$

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How do you multiply $(9 a + 2) (9 a^{2} + a + 1)$ $(9a +2) (9a^2 + a + 1)$ ?

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How do you multiply $(9 a + 2) (9 a^{2} + a + 1)$ $(9a +2) (9a^2 + a + 1)$ ?