Sure, let's multiply the expressions [tex]\((5x - 3w)(x - 7w)\)[/tex] step-by-step.
1. Distribute each term from the first binomial to each term in the second binomial:
- Multiply the first term in the first binomial with each term in the second binomial:
[tex]\[
(5x) \cdot (x) = 5x^2
\][/tex]
[tex]\[
(5x) \cdot (-7w) = -35xw
\][/tex]
- Multiply the second term in the first binomial with each term in the second binomial:
[tex]\[
(-3w) \cdot (x) = -3wx
\][/tex]
[tex]\[
(-3w) \cdot (-7w) = 21w^2
\][/tex]
2. Write down all the products:
[tex]\[
5x^2 - 35xw - 3wx + 21w^2
\][/tex]
3. Combine the like terms:
[tex]\[
-35xw \text{ and } -3wx
\][/tex]
Notice that [tex]\(-35xw\)[/tex] and [tex]\(-3wx\)[/tex] are like terms (since they both contain [tex]\(xw\)[/tex]), so we can add them:
[tex]\[
-35xw - 3wx = -38xw
\][/tex]
4. Write the simplified expression:
[tex]\[
5x^2 - 38xw + 21w^2
\][/tex]
So, the product of [tex]\((5x - 3w)\)[/tex] and [tex]\((x - 7w)\)[/tex] is:
[tex]\[
5x^2 - 38xw + 21w^2
\][/tex]
