Question

Expand and simplify: (ab+12a)(12a+ab+b)

Answer 1

To expand and simplify (ab+12a)(12a+ab+b), apply the distributive property to multiply the terms and combine like terms to get the simplified expression 24a^2b + a^2b^2 + ab^2 + 144a^2 + 12ab.

Step-by-step explanation:

Expanding and Simplifying Binomials

To expand and simplify the expression (ab+12a)(12a+ab+b), we will use the distributive property, also known as the FOIL method for binomials. The steps are as follows:

1. Multiply each term in the first binomial by each term in the second binomial.
2. Combine like terms.
3. Simplify the expression if possible.

Expanding the given expression:

(ab + 12a)(12a + ab + b)

= ab(12a) + ab(ab) + ab(b) + 12a(12a) + 12a(ab) + 12a(b)

Now, we combine like terms and simplify the expression.

= 12a2b + a2b2 + ab2 + 144a2 + 12a2b + 12ab

Combine like terms:

= (12a2b + 12a2b) + a2b2 + ab2 + 144a2 + 12ab

= 24a2b + a2b2 + ab2 + 144a2 + 12ab

This is the expanded and simplified form of the original expression.