Question

What is the number of terms in the expansion {[2x-3y]^2 [2x+3y]^2}^2?

Answer 1

Answer:

The given expression has a number of terms of expansion = 6.

Step-by-step explanation:

We have to find the number of terms in the expansion

$\{[2x-3y]^2\times[2x+3y]^2\}^2$

Expanding the above expression we  get

$\{ [2x - 3y]\times [2x + 3y] \times [2x - 3y] \times [2x + 3y]\}^2$

In the above we can see that we can use the algebraic equation where

$(a+b)(a-b) = a^2 - b^2$

= $\{ (4x^2 - 9y^2) (4x^2 - 9y^2)\}^2$

= $\{ 16x^4 - 72x^2y^2 + 81y^4\}^2$

= $256x^8 + 5184x^4y^4 + 6561y^8 - 2304x^6y^2 -11664 x^2y^6 + 2592x^4y^4$

The last part of the expansion can be found from the algebraic formula

$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ac$

So we can see the number of terms of the expansion is 6.