Question

Expand (2x -3y)^5 using the given formula.

Answer 1

(2x-3y)^5

(2x-3y)(2x-3y)(2x-3y)(2x-3y)(2x-3y)

1st and 2nd power :
(2x-3y)(2x-3y) = 2x(2x-3y)-3y(2x-3y) = 4x² - 6xy - 6xy + 9y²
= 4x² - 12xy + 9y²

3rd power:
(2x-3y)(4x² - 12xy + 9y²) = 2x(4x² - 12xy + 9y²) - 3y(4x² - 12xy + 9y²)
8x³ - 24x²y + 18xy² - 12x²y +36xy² - 27y³
8x³ - 24x²y - 12x²y + 18xy² + 36xy² - 27y³
8x³ - 36x²y + 54xy² - 27y³

4th power
(2x-3y)(8x³ - 36x²y + 54xy² - 27y³) = 2x(8x³ - 36x²y + 54xy² - 27y³) -3y(8x³ - 36x²y + 54xy² - 27y³) = 16x^4 - 72x³y + 108x²y² - 54xy³ - 24x³y + 108x²y² - 162xy³ + 81y^4
16x^4 - 72x³y - 24x³y + 108x²y² + 108x²y² - 54xy³ - 162xy³ + 81y^4
16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4

5th power
(2x-3y)(16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
2x(16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4) - 3y(16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
= 32x^5 - 192x^4y + 432x³y² - 432x²y³ + 162xy^4 - 48x^4y + 288x³y² - 648x²y³ + 648xy^4 - 243y^5

32x^5 - 192x^4y -48x^4y + 432x³y² + 288x³y² - 432x²y³ - 648x²y³ + 162xy^4 + 648xy^4 - 243y^5

32x^5 - 240x^4y + 720x³y² - 1,080x²y³ + 810xy^4 - 243y^5