Question

Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4

Answer 1

Explanation:

Binomial Expansion:

`(2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4`

Pascal's Triangle:

Zero row 1

First row 1 1

Second row 1 2 1

Third row 1 3 3 1

Fourth row 1 4 6 4 1