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

Sagot :

MrRoyalidn

Answer:

(a) [tex]3a^4 - 11a^2b^2 -2b^4[/tex]

(b) [tex]3a^4 - 11a^2b^2 -2b^4= 2[/tex]

Step-by-step explanation:

Given

[tex](a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)[/tex]

Solving (a): Simplify

[tex](a^4 - 6a^2b^2+ b^4) - (-2a^4+5a^2b^2+ 3b^4)[/tex]

Open brackets

[tex]a^4 - 6a^2b^2+ b^4 +2a^4-5a^2b^2- 3b^4[/tex]

Collect Like Terms

[tex]a^4 +2a^4- 6a^2b^2-5a^2b^2+ b^4 - 3b^4[/tex]

Simplify Like Terms

[tex]3a^4 - 11a^2b^2 -2b^4[/tex]

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

[tex]3a^4 - 11a^2b^2 -2b^4[/tex]

[tex]3*(2)^4 - 11*(2^2)*(-1)^2 -2*(-1)^4[/tex]

[tex]3 * 16 - 11 * 4 * 1 - 2 * 1[/tex]

[tex]48 - 44 - 2[/tex]

[tex]= 2[/tex]

Hence:

[tex]3a^4 - 11a^2b^2 -2b^4= 2[/tex]

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