Questions: Polynomials and Factoring Multiplying binomials with leading coefficients greater than 1 Multiply. (5c-1)(8c-5) Simplify your answer.

Solution Steps

To multiply the binomials \((5c - 1)(8c - 5)\), we will use the distributive property (also known as the FOIL method for binomials). This involves multiplying each term in the first binomial by each term in the second binomial and then combining like terms.

To multiply \((5c - 1)(8c - 5)\), we start by distributing each term in the first binomial to each term in the second binomial: \[ (5c - 1)(8c - 5) = 5c \cdot 8c + 5c \cdot (-5) + (-1) \cdot 8c + (-1) \cdot (-5) \]

Next, we perform the multiplications: \[ 5c \cdot 8c = 40c^2 \] \[ 5c \cdot (-5) = -25c \] \[ -1 \cdot 8c = -8c \] \[ -1 \cdot (-5) = 5 \]

Now, we combine the like terms: \[ 40c^2 - 25c - 8c + 5 \] \[ 40c^2 - 33c + 5 \]

Final Answer