Question
Factorize:
a2 + b2 + 2(ab + bc + ca)
a2 + b2 + 2(ab + bc + ca)
✓
Answer
= a2 + b2 + 2ab + 2bc + 2ca
Using the identity (p + q)2 = p2 + q2 + 2pq
We get,
= (a + b)2 + 2bc + 2ca
= (a + b)2 + 2c(b + a)
Or (a + b)2 + 2c(a + b)
Taking (a + b) common
= (a + b)(a + b + 2c)
$\therefore$ a2 + b2 + 2(ab + bc + ca) = (a + b)(a + b + 2c)
Using the identity (p + q)2 = p2 + q2 + 2pq
We get,
= (a + b)2 + 2bc + 2ca
= (a + b)2 + 2c(b + a)
Or (a + b)2 + 2c(a + b)
Taking (a + b) common
= (a + b)(a + b + 2c)
$\therefore$ a2 + b2 + 2(ab + bc + ca) = (a + b)(a + b + 2c)
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