When multiplying two binomials (expressions with two terms), you can use the FOIL method. Our two binomials are (3x - 7) and (3x - 5).
See picture. FOIL is an acronym for First, Outside, Inside, Last. Add the products of the first, outside, inside, and last terms of each binomial to multiply binomials.
For this problem:
1) Multiply the first terms, 3x and 3x.
[tex]3x(3x) = 9 x^{2} [/tex]
2) Multiply the outside terms:
[tex]3x(-5) = -15x[/tex]
3) Multiply the inside terms:
[tex]-7(3x) = -21x[/tex]
4) Multiply the last terms:
[tex]-7(-5) = 35[/tex]
5) Add all the products from FOILing together:
[tex]9 x^{2} + (- 15x) + (-21x) + 35\\
= 9 x^{2} - 15x -21x + 35\\
= 9 x^{2} - 36x + 35[/tex]
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Answer: D) [tex]9 x^{2} - 36x + 35[/tex]
