Question

Simplify the expression(a4−6a2b2+ b4)−(−2a4+5a2b2+ 3b4) and hence, find its value for a = 2and b = −1.

Answer 1

(a)
`3a^4 - 11a^2b^2 -2b^4`

(b)
`3a^4 - 11a^2b^2 -2b^4= 2`

Explanation:

Given

`(a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)`

Solving (a): Simplify

`(a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)`

Open brackets

`a^4 - 6a^2b^2+ b^4 +2a^4-5a^2b^2- 3b^4`

Collect Like Terms

`a^4 +2a^4- 6a^2b^2-5a^2b^2+ b^4 - 3b^4`

Simplify Like Terms

`3a^4 - 11a^2b^2 -2b^4`

Solving (b): Simplify when a = 2 and b = -1

`3a^4 - 11a^2b^2 -2b^4`

`3*(2)^4 - 11*(2^2)*(-1)^2 -2*(-1)^4`

`3 * 16 - 11 * 4 * 1 - 2 * 1`

`48 - 44 - 2`

`= 2`

Hence:

`3a^4 - 11a^2b^2 -2b^4= 2`