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

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Answer 1 · 2017-04-16T20:50:44

#a^2 +8ab + 16b^2#

#(a + 4b)^2 = (a + 4b) (a + 4b)#

Use the exponent rule #x*x = x^1x^1 = x^(1+1) = x^2#

Use the commutative property of multiplication: #a*b = b*a#

Use distribution to multiply:

#(a + 4b)^2 = a*a + a*4b + 4b*a + 4b*4b#

#= a^2 + 4ab + 4ab + 16b^2#

#=a^2 +8ab + 16b^2#