Sure, let's multiply the given binomials:
First, we have:
[tex]\[
(4x - 5z)(x + 7z)
\][/tex]
To multiply these expressions, we'll use the distributive property (also known as the FOIL method for binomials), which involves multiplying each term in the first binomial by each term in the second binomial.
Step-by-step:
1. Multiply the first terms in each binomial:
[tex]\[
4x \cdot x = 4x^2
\][/tex]
2. Multiply the outer terms in each binomial:
[tex]\[
4x \cdot 7z = 28xz
\][/tex]
3. Multiply the inner terms in each binomial:
[tex]\[
-5z \cdot x = -5xz
\][/tex]
4. Multiply the last terms in each binomial:
[tex]\[
-5z \cdot 7z = -35z^2
\][/tex]
Now, combine all these results together:
[tex]\[
4x^2 + 28xz - 5xz - 35z^2
\][/tex]
Next, combine the like terms (the [tex]\(xz\)[/tex] terms):
[tex]\[
28xz - 5xz = 23xz
\][/tex]
Therefore, the fully simplified result of multiplying the two binomials is:
[tex]\[
4x^2 + 23xz - 35z^2
\][/tex]
