How do you multiply #(x+4)^3#?

2 Answers
marfre
Jul 4, 2018

#x^3 + 12x^2 + 48x + 64#

Explanation:

Given: #(x + 4)^3#

#(x + 4)^3 = (x+4)(x+4)(x+4)#

Using foil and #(a + b)^2 = a^2 + 2ab + b^2#:

#(x + 4)^3 = (x^2 + 8x + 16)(x+4)#

# = x^3 + 8x^2 + 16x + 4x^2 + 32x + 64#

Add like terms:

#(x + 4)^3 = x^3 + 12x^2 + 48x + 64#

Jim G.
Jul 4, 2018

#x^3+12x^2+48x+64#

Explanation:

#"given a factor "(x+a)^3" the expansion is"#

#x^3+(a+a+a)x^2+(a^2+a^2+a^2)x+a^3#

#"here "a=4#

#(x+4)^3#

#=x^3+(4+4+4)x^2+(4^2+4^2+4^2)x+4^3#

#=x^3+12x^2+(16+16+16)x+64#

#=x^3+12x^2+48x+64#

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