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Mathematics
Kaleigh
22 September, 12:34
Factorize a^2+b^2+2 (ab-ac-bc)
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Lillianna Mercer
22 September, 13:03
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(a + b) (a + b - 2c)
Step-by-step 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
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