Sure, let's find the product of the two binomials [tex]\( (x + 3) \)[/tex] and [tex]\( (x - 7) \)[/tex].
1. Distribute [tex]\( x \)[/tex] from the first binomial to both terms in the second binomial:
[tex]\[
x \cdot (x - 7) = x^2 - 7x
\][/tex]
2. Distribute [tex]\( 3 \)[/tex] from the first binomial to both terms in the second binomial:
[tex]\[
3 \cdot (x - 7) = 3x - 21
\][/tex]
3. Combine all the terms together:
[tex]\[
x^2 - 7x + 3x - 21
\][/tex]
4. Combine like terms (the [tex]\( -7x \)[/tex] and the [tex]\( 3x \)[/tex]):
[tex]\[
x^2 - 4x - 21
\][/tex]
So, the product of the binomials [tex]\( (x + 3)(x - 7) \)[/tex] is:
[tex]\[
x^2 - 4x - 21
\][/tex]
