Question

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

Answer 1

Answer:

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

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

Step-by-step 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:

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