Given:
[tex](5x-2y)^4[/tex]
Below is a Pascal's Triangle.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
Since the exponent we have is 4, counting from zero , we need the last row to expand.
Since the second term in the parenthesis is negative, we shall alternate the sign.
We can now begin the expansion;
(5x - 2y)⁴ = (5x)⁴(2y)⁰ - (5x)³(2y)¹ + (5x)²(2y)² - (5x)¹(2y)³ + (5x)⁰ (2y)⁴
= 625x⁴(1) - 125x³(2y) + 25x² (4y²) - 5x(8y³) + 1(16y⁴)
= 625x⁴ - 250x³y + 100x²y² - 40xy³ + 16y⁴
