simplify the following expression without using calculator.
-2(-4a squared + b cube) square
........
-2 (-4a squared + b cube)(-4a squared + b cube)
-2 (16a square - 4a square b cube + b cube)
-2 (+ 16 a square = b cube )
-32a square - 2b cube.
See my reply to your other post
http://www.jiskha.com/display.cgi?id=1422164761
To simplify the given expression without using a calculator, follow these steps:
1. Start with the original expression: -2(-4a^2 + b^3)^2.
2. Square the binomial inside the parentheses: (-4a^2 + b^3)^2 = (-4a^2 + b^3)(-4a^2 + b^3).
3. Apply the distributive property to expand the expression: -2(-4a^2)(-4a^2) + (-2)(-4a^2)(b^3) + (-2)(b^3)(-4a^2) + (-2)(b^3)(b^3).
4. Simplify each term within the expanded expression: 16a^4 + 8a^2b^3 + 8a^2b^3 + 2b^6.
5. Combine like terms: 16a^4 + 16a^2b^3 + 2b^6.
6. Distribute the negative sign outside the entire expression: -16a^4 - 16a^2b^3 - 2b^6.
7. Finally, the simplified expression is -16a^4 - 16a^2b^3 - 2b^6.