How do you find the product of #(x + 7)² #?

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Answer 1 · 2017-05-27T18:05:55

FOIL

FOIL stands for First Outside Inside Last

#(x+7)^2#

This can be rewritten as:

#(x+7)(x+7)#

Multiply the first terms in each expression.

#(color(blue)(x)+7)(color(blue)(x)+7)#

#color(blue)(x*x = x^2)#

Now we move to outside . multiply the outside terms of each expression.

#(color(orange)(x^2)+7)(x^2+color(orange)(7))#

#color(orange)(x^2 * 7 = 7x^2)#

Next up are the inside terms. Multiply these from each expression.

#(x^2 + (color(green)(7))) (color(green)(x^2) + 7)#

#color(green)(7 * x^2 = 7x^2#

Finally, we have the last terms. Multiply the last terms from each expression.

#(x^2 + color(red)(7))(x^2 + color(red)(7))#

#color(red)(7*7 = 49#

Now combine all of the solutions that we have come up with.

#color(blue)(x^2) + color(orange)(7x^2) + color(green)(7x^2)+ color(red)(49)#

Combine the like terms in between.

#x^2 + 14x + 49#