Questions: Multiply the polynomials using the distributive property and combine like terms. (x+4)(x+6) Answer x^2+10x+24

Solution Steps

To multiply the polynomials \((x+4)(x+6)\) using the distributive property, we need to apply the distributive property (also known as the FOIL method for binomials) to each term in the first polynomial by each term in the second polynomial. Then, we combine like terms to simplify the expression.

We start with the polynomials \((x + 4)\) and \((x + 6)\). Using the distributive property, we multiply each term in the first polynomial by each term in the second polynomial:

\[ (x + 4)(x + 6) = x \cdot x + x \cdot 6 + 4 \cdot x + 4 \cdot 6 \]

Calculating each term, we have:

\[ x^2 + 6x + 4x + 24 \]

Now, we combine the like terms \(6x\) and \(4x\):

\[ x^2 + (6x + 4x) + 24 = x^2 + 10x + 24 \]

Final Answer