Questions: Multiply. (x+4z)(6x-5z) Simplify your answer.

Transcript text: Multiply. \[ (x+4 z)(6 x-5 z) \] Simplify your answer.

Solution

Solution Steps

To multiply the binomials \((x + 4z)(6x - 5z)\), 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.

Step 1: Multiply the Binomials

We start with the binomials \((x + 4z)\) and \((6x - 5z)\). Using the distributive property, we multiply each term in the first binomial by each term in the second binomial:

\[ (x + 4z)(6x - 5z) = x \cdot 6x + x \cdot (-5z) + 4z \cdot 6x + 4z \cdot (-5z) \]

Step 2: Calculate Each Term

Calculating each term gives us:

\[ = 6x^2 - 5xz + 24xz - 20z^2 \]

Step 3: Combine Like Terms

Now, we combine the like terms \(-5xz\) and \(24xz\):

\[ = 6x^2 + (24 - 5)xz - 20z^2 = 6x^2 + 19xz - 20z^2 \]