Questions: Multiply the polynomial by the monomial using the distributive property and/or the product rule of exponents. (y)(6xy-2x+7)

Solution Steps

To multiply the polynomial by the monomial, apply the distributive property. This involves multiplying each term in the polynomial by the monomial. Additionally, use the product rule of exponents, which states that when multiplying like bases, you add the exponents.

We start with the expression \( (y)(6xy - 2x + 7) \). Here, \( y \) is the monomial and \( 6xy - 2x + 7 \) is the polynomial.

Using the distributive property, we multiply \( y \) by each term in the polynomial: \[ y \cdot (6xy) + y \cdot (-2x) + y \cdot 7 \]

Calculating each term gives us:

• \( y \cdot (6xy) = 6xy^2 \)
• \( y \cdot (-2x) = -2xy \)
• \( y \cdot 7 = 7y \)

Combining all the terms results in: \[ 6xy^2 - 2xy + 7y \]

Final Answer