Certainly! Let's multiply the expressions [tex]\((4x + 3)\)[/tex] and [tex]\((7x - 1)\)[/tex] and fully simplify.
To multiply two binomials, we use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, and Last). Here's a step-by-step breakdown:
1. First: Multiply the first terms in each binomial.
[tex]\[
4x \cdot 7x = 28x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials.
[tex]\[
4x \cdot (-1) = -4x
\][/tex]
3. Inner: Multiply the inner terms in the binomials.
[tex]\[
3 \cdot 7x = 21x
\][/tex]
4. Last: Multiply the last terms in each binomial.
[tex]\[
3 \cdot (-1) = -3
\][/tex]
Next, we combine all the terms:
[tex]\[
28x^2 + (-4x) + 21x + (-3)
\][/tex]
Now, combine the like terms (i.e., the terms involving [tex]\(x\)[/tex]):
[tex]\[
28x^2 + 17x - 3
\][/tex]
Thus, the product of [tex]\((4x + 3)\)[/tex] and [tex]\((7x - 1)\)[/tex], when simplified, is:
[tex]\[
\boxed{28x^2 + 17x - 3}
\][/tex]
