**Find the coefficient of x**^{2} expansion of (x^{2} + x + 1)^{2} + (x^{2} – x + 1)^{2}

^{2}expansion of (x

^{2}+ x + 1)

^{2}+ (x

^{2}– x + 1)

^{2}

**Answer :**

Given:

The expression, (x^{2} + x + 1)^{2} + (x^{2} – x + 1)^{2}

(x^{2} + x + 1)^{2} + (x^{2} – x + 1)^{2} = [((x^{2} + 1) + x)^{2} + [(x^{2} + 1) – x)^{2}]

= (x^{2} + 1)^{2} + x^{2} + 2 (x^{2} + 1) (x) + (x^{2} + 1)^{2} + x^{2} – 2 (x^{2} + 1) (x)

= (x^{2})^{2} + (1)^{2} + 2 × x^{2} × 1 + x^{2} + (x^{2})^{2} + 1 + 2 × x^{2} + 1 + x^{2}

= x^{4} + 1 + 2x^{2} + x^{2} + x^{4} + 1 + 2x^{2} + x^{2}

= 2x^{4} + 6x^{2} + 2

∴ Co-efficient of x^{2} is 6.

**More Solutions:**

- Factories the following :
- Factorise 21py2 – 56py
- Factorise 2πr2 – 4πr
- Factorise 25abc2 – 15a2b2c
- Factorise 8×3 – 6×2 + 10x
- Factorise 18p2q2 – 24pq2 + 30p2q
- Factorise 15a (2p – 3q) – 10b (2p – 3q)
- Factorise 6(x + 2y)3 + 8(x +2y)2
- Factorise 10a(2p + q)3 – 15b (2p + q)2 + 35 (2p + q)
- Factorise x2 + xy – x – y
- Factorise 5xy + 7y – 5y2 – 7x