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Simplify ​(1.5a2−2.5b2)(1.5a2+2.5b2)+6.25ab(1.5a^2 - 2.5b^2)(1.5a^2 + 2.5b^2) + 6.25ab(1.5a2−2.5b2)(1.5a2+2.5b2)+6.25ab​​
Question

Simplify
(1.5a22.5b2)(1.5a2+2.5b2)+6.25ab(1.5a^2 - 2.5b^2)(1.5a^2 + 2.5b^2) + 6.25ab​​

A.

2.25a46.25b42.25a^4-6.25b^4​​

B.

2.25a46.5b4+6.25ab2.25a^4-6.5b^4+6.25ab​​

C.

2.5a46.25b4+6.25ab2.5a^4-6.25b^4+6.25ab​​

D.

2.25a46.25b4+6.25ab2.25a^4-6.25b^4+6.25ab​​

Correct option is D

Given:

(1.5a22.5b2)(1.5a2+2.5b2)+6.25ab(1.5a^2 - 2.5b^2)(1.5a^2 + 2.5b^2) + 6.25ab​​

Formula Used:

(xy)(x+y)=x2y2(x - y)(x + y) = x^2 - y^2 ​​

Solution:

x = 1.5a2 & y = 2.5b2 

using this in given equation;

(1.5a2)2(2.5b2)2+6.25ab =2.25a46.25b4+6.25ab(1.5a^2)^2 - (2.5b^2)^2 + 6.25ab\\ \ \\ = 2.25a^4 - 6.25b^4 + 6.25ab ​​


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