How do you find the product ${(a + 4 b)}^{2}$ $(a+4b)^2$ ?

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Answer 1 · 2017-04-16T20:50:44

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

${(a + 4 b)}^{2} = (a + 4 b) (a + 4 b)$ $(a + 4b)^2 = (a + 4b) (a + 4b)$

Use the exponent rule $x \cdot x = x^{1} x^{1} = x^{1 + 1} = x^{2}$ $x*x = x^1x^1 = x^(1+1) = x^2$

Use the commutative property of multiplication: $a \cdot b = b \cdot a$ $a*b = b*a$

Use distribution to multiply:

${(a + 4 b)}^{2} = a \cdot a + a \cdot 4 b + 4 b \cdot a + 4 b \cdot 4 b$ $(a + 4b)^2 = a*a + a*4b + 4b*a + 4b*4b$

$= a^{2} + 4 a b + 4 a b + 16 b^{2}$ $= a^2 + 4ab + 4ab + 16b^2$

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

How do you find the product (a+4b)^2(a+4b)2(a+4b)^2?