use the pascal s tringle to find the expansion of (2x -5) to the power 4

Answer 1

To expand (2x - 5) to the power of 4 using Pascal's Triangle, we can use the binomial theorem.

Pascal's Triangle for finding the coefficients of binomial expansions has the following pattern:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

To find the expansion of (2x - 5)^4, we can use the coefficients from the 5th row of Pascal's Triangle (starting with 1) to find the terms:

(2x)^4 = 16x^4
(2x)^3 * -5 = -40x^3
(2x)^2 * (-5)^2 = 100x^2
(2x) * (-5)^3 = -250x
(-5)^4 = 625

Now, we combine these terms using the coefficients from Pascal's Triangle:

16x^4 - 40x^3 + 100x^2 - 250x + 625

Therefore, the expansion of (2x - 5)^4 is 16x^4 - 40x^3 + 100x^2 - 250x + 625.