Find each product. (5m-6)(3m+4)

Verified step by step guidance

1. Identify the two binomials to be multiplied: \((5m - 6)\) and \((3m + 4)\).
2. Apply the distributive property (also known as the FOIL method) to multiply each term in the first binomial by each term in the second binomial: First, Outer, Inner, Last.
3. Multiply the First terms: \$5m \times 3m = 15m^{2}$.
4. Multiply the Outer terms: \$5m \times 4 = 20m$.
5. Multiply the Inner terms: \(-6 \times 3m = -18m\), and the Last terms: \(-6 \times 4 = -24\). Then combine like terms \$20m\( and \)-18m$.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, a(b + c) = ab + ac. This property is essential for expanding expressions like (5m - 6)(3m + 4) by multiplying each term in the first parenthesis by each term in the second.

Multiplying Binomials

Multiplying binomials involves applying the distributive property twice or using the FOIL method (First, Outer, Inner, Last) to multiply each term in the first binomial by each term in the second. This process results in a polynomial expression.

Combining Like Terms

After multiplying, you often get terms with the same variable and exponent. Combining like terms means adding or subtracting these terms to simplify the expression into its simplest polynomial form.