Question

Muliply the monomial and the polynomial. -5a^(4)b^(3)(2a^(2)b^(3)-a+6b^(3))

Answer 1

To multiply a monomial and a polynomial, distribute the monomial to every term in the polynomial. In this case, the monomial is -5a⁴b³and the polynomial is 2a²b³ - a + 6b³.

Step-by-step explanation:

To multiply a monomial and a polynomial, you need to distribute the monomial to every term in the polynomial. In this case, the monomial is -5a⁴b³ and the polynomial is 2a²b³ - a + 6b³.

The first term of the polynomial, 2a²b³, when multiplied by the monomial, becomes -10a6b6 (multiply the coefficients and add the exponents of the variables).

The second term, -a, when multiplied by the monomial, becomes 5a5b³.

The third term, 6b3, when multiplied by the monomial, becomes -30a⁴b⁶.

So the multiplication of the monomial and the polynomial is -10a⁶b⁶ + 5a5b³ - 30a⁴b⁶.