SOLUTION: Explain in your own words why (a+b)^2 is not equal to a^2 + b^2? What does (a+b)^2 and (a-b)^2 equal?

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Question 423854: Explain in your own words why (a+b)^2 is not equal to a^2 + b^2?
What does (a+b)^2 and (a-b)^2 equal?
Answer by algebrahouse.com(1659) About Me  (Show Source):
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"Explain in your own words why (a+b)^2 is not equal to a^2 + b^2?
What does (a+b)^2 and (a-b)^2 equal?"

You are squaring two different binomials.
When you square a binomial, you multiply it by itself.

(a + b)^2
= (a + b)(a + b)
= a(a) + a(b) + b(a) + b(b) {used foil method}
= a^2 + ab + ab + b^2 {multiplied through}
= a^2 + 2ab + b^2 {combined like terms}

(a - b)^2
= (a - b)(a - b)
= a(a) + a(-b) - b(a) - b(-b) {used foil method}
= a^2 - ab - ab + b^2 {multiplied through}
= a^2 - 2ab + b^2 {combined like terms}
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