Question

Expand and simplify
4a^2(b^2-c)+2ab(ab-c)-ac(a+2b)

Answer 1

4a²(b² - c) + 2ab(ab - c) - ac(a + 2b)
4a²(b²) - 4a²(c) + 2ab(ab) - 2ab(c) - ac(a) - ac(2b)
4a²b² - 4a²c + 2a²b² - 2abc - a²c - 2abc
4a²b² + 2a²b² - 4a²c - a²c - 2abc - 2abc
6a²b² - 5a²c - 4abc

Answer 2

`4a^2(b^2-c)+2ab(ab-c)-ac(a+2b)\\-----------------------\\use\ distributive\ property:a(b-c)=ab+ac\\-----------------------\\=4a^2b^2-4a^2c+2a^2b^2-2abc-a^2c-2abc\\=(4a^2b^2+2a^2b^2)+(-4a^2c-a^2c)+(-2abc-2abc)\\\\=\boxed{6a^2b^2-5a^2c-4abc}`