Question

Simplify 4a^2b - (a^2 - b)^2

Answer 1

Answer:

$\LARGE{ \underline{\underline{ \pink{ \bf{Required \: answer:}}}}}$

1) Expand the square

4a²b - 1 ( a² - b)²

4a²b - 1 ( a² - b) - ( a² - b)

2) Distribute

4a²b - 1 (a² - b)(a² - b)

4a²b - 1 (( a² - b ) . a² - b( a² - b ))

3) Distribute

4a²b - 1 (( a² - b ) . a² - b( a² - b ))

4a²b - 1 ( a⁴ - ba² - b(a² - b))

4) Distribute

4a²b - 1 ( a⁴ - ba² - b(a² - b))

4a²b - 1 ( a⁴ - ba² - ba² + b²)

5) Combine like terms:

4a²b - 1 ( a⁴ - ba² - ba² + b²)

4a²b - 1 ( a⁴ - 2ab² + b²)

6) Distribute:

4a²b - 1 ( a⁴ - 2ab² + b²)

4a²b-1a⁴ + 2ab² - 1b²

7) Rearrange Terms:

4a²b-1a⁴ + 2ab² - 1b²

-1a⁴ + a²b + 2ab² - 1b²

$\huge\orange{Solution}$

-1a⁴ + a²b + 2ab² - 1b²