how can i solve this equation:
(a-b)(2a-b)(a+2b)
can anyone be so kind to help me with it?
p.s.
I'm barely learning
how to multiply polynomials.
http://www.purplemath.com/modules/polymult.htm
Of course! I'd be happy to help you solve this equation.
The expression you provided is not an equation but a polynomial expression. To solve it, we can simplify and expand the expression using the distributive property of multiplication.
First, let's expand the product by multiplying each pair of terms:
(a - b)(2a - b)(a + 2b)
= (a * 2a * a) + (a * 2a * 2b) + (a * -b * a) + (a * -b * 2b) + (-b * 2a * a) + (-b * 2a * 2b) + (-b * -b * a) + (-b * -b * 2b)
Next, we can simplify each term:
= 2a^3 + 4a^2b + (-a^2b) + (-2ab^2) + (-2a^2b) + (-4ab^2) + ab^2 + 2b^3
Now, let's combine like terms by adding or subtracting coefficients of the same variable and exponent:
= 2a^3 + (-a^2b + (-2a^2b) + 4a^2b) + (ab^2 + (-2ab^2 - 4ab^2)) + 2b^3
= 2a^3 + (-a^2b + (-2a^2b) + 4a^2b) + (ab^2 - 6ab^2) + 2b^3
= 2a^3 + a^2b + (-6ab^2) + 2b^3
So, the simplified form of the polynomial expression is:
2a^3 + a^2b - 6ab^2 + 2b^3
This is the final answer.
I hope this helps you understand how to multiply polynomials. If you have any further questions, feel free to ask!