How do you simplify #(x + 3) ^ { 2} - ( x + 1) ^ { 2}#?

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Answer 1 · 2017-03-04T14:47:09

See the entire simplification process below:

First, use this rule to expand the terms within parenthesis:

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

#(x + 3)^2 - (x + 1)^2#

#(x^2 + 6x + 9) - (x^2 + 2x + 1)#

Next, remove all the terms from parenthesis and group like terms:

#x^2 + 6x + 9 - x^2 - 2x - 1#

#x^2 - x^2 + 6x - 2x + 9 - 1#

Now, combine like terms:

#(x^2 - x^2) + (6 - 2)x + 8#

#0 + 4x + 8#

#4x + 8#

Or

#4(x + 2)#