Question

How do you multiply \[(a + 2b - 4ab)(2a - b)\]?

Answer 1

Hint: Here in this question we are asked to multiply two polynomials. So firstly we will multiply each term of the first polynomial with each term of the other polynomial. We will multiply the coefficient (numbers) and add the exponents while multiplying two terms together. Further if there is required then we will simplify the equation.

Complete step-by-step solution:
Firstly we will multiply each term in the first expression with each term in the second expression and expand the given equation\[(a + 2b - 4ab)(2a - b)\].
By using commutative property of multiplication we get
\[\Rightarrow a(2a) + a( - b) + 2b(2a) + 2b( - b) - 4ab(2a) - 4ab( - b)\]
Later on simplifying we get
\[\Rightarrow 2{a^2} - ab + 4ba - 2{b^2} - 8{a^2}b + 4a{b^2}\]
Now in order to combine like terms we will add \[ - ab\]and \[4ba\]
\[\Rightarrow 2{a^2} + 3ab - 2{b^2} - 8{a^2}b + 4a{b^2}\]
Lastly after simplification the answer will be
\[\Rightarrow - 8{a^2}b + 4a{b^2} + 2{a^2} + 3ab - 2{b^2}\]

Thus the final answer \[ - 8{a^2}b + 4a{b^2} + 2{a^2} + 3ab - 2{b^2}\]

Additional Information: Multiplication can be done in any order in which each of the first two terms is multiplied with each of the second two terms and in the final answer correctness of the solution is not affected by order of terms.

Note: Keep in mind that we have used distributive law of multiplication while solving the above question as it is used for multiplying polynomials. Then we combined the like terms for reducing the expected number of products . Lastly remember we need to write the decreasing order of their exponent.