To solve the expression [tex]\((3x - 6)(7x + 7)\)[/tex], we need to expand it step-by-step by using the distributive property (also known as the FOIL method for binomials). Here is the detailed process:
1. Expand each term: Apply the distributive property, where each term in the first binomial is multiplied by each term in the second binomial.
[tex]\[ (3x - 6)(7x + 7) \][/tex]
- Multiply the first terms:
[tex]\[ 3x \cdot 7x = 21x^2 \][/tex]
- Multiply the outer terms:
[tex]\[ 3x \cdot 7 = 21x \][/tex]
- Multiply the inner terms:
[tex]\[ -6 \cdot 7x = -42x \][/tex]
- Multiply the last terms:
[tex]\[ -6 \cdot 7 = -42 \][/tex]
2. Combine like terms: Add together all the products from the previous step.
[tex]\[
21x^2 + 21x - 42x - 42
\][/tex]
3. Simplify the expression: Combine the like terms [tex]\(21x\)[/tex] and [tex]\(-42x\)[/tex].
[tex]\[
21x^2 + (21x - 42x) - 42
\][/tex]
This simplifies to:
[tex]\[
21x^2 - 21x - 42
\][/tex]
Therefore, the expanded form of the expression [tex]\((3x - 6)(7x + 7)\)[/tex] is:
[tex]\[
21x^2 - 21x - 42
\][/tex]
