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Factorize a^2+b^2+2(ab-ac-bc)

1 Answer

4 votes

Answer:

(a + b)(a + b - 2c)

Explanation:

Note that

(a + b)² = a² + b² + 2ab

Given

a² + b² + 2(ab - ac - bc) ← distribute parenthesis

= a² + b² + 2ab - 2ac - 2bc

= (a + b)² - 2ac - 2bc ← factor out - 2c from each term

= (a + b)² - 2c (a + b) ← factor out (a + b) from each term

= (a + b) [ a + b - 2c ]

= (a + b)(a + b - 2c) ← in factored form

User Paul Hoffer
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