Maharashtra State BoardSSC (English Medium) 8th Standard

Expansion of (a + b + c)2

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Formula

  • (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.

Notes

Expansion of (a + b + c)2:

(a + b + c)2 = (a + b + c) × (a + b + c).

(a + b + c)2 = a(a + b + c) + b(a + b + c) + c(a + b + c).

(a + b + c)2 = a2 + ab + ac + ab + b2 + bc + ac + bc + c2.

(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.

∴ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac.

Example

Expand: (p + q + 3)2

(p + q + 3)

= p2 + q2 + (3)2 + 2 × p × q + 2 × q × 3 + 2 × p × 3

= p2 + q2 + 9 + 2pq + 6q + 6p

= p2 + q2 + 2pq + 6q + 6p + 9.

Example

Simplify: (l + 2m + n)2 + (l - 2m + n)2.

(l + 2m + n)2 + (l - 2m + n)2

= l2 + 4m2 + n2 + 4lm + 4mn + 2ln + l2 + 4m2 + n2 - 4lm - 4mn + 2ln

= 2l2 + 8m2 + 2n2 + 4ln

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