How do you simplify: #3 - (2x - 9)^2#?

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Answer 1 · 2017-07-18T12:20:52

See a solution process below:

First, expand the term in parenthesis with the exponent using this rule for quadratics:

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

Substitute #2x# for #a# and #9# for #b# giving:

#3 - (2x - 9)^2 => 3 - ((2x)^2 - (2 * 2x * 9) + 9^2) =>#

#3 - (4x^2 - 36x + 81)#

Next, remove the terms from parenthesis being careful to manage the signs of the individual terms correctly:

#3 - 4x^2 + 36x - 81#

Now, group and combine the like terms, which in this problem are the constants:

#-4x^2 + 36x - 81 + 3 =>#

#-4x^2 + 36x - 78#