Question Multiply the expression $(7 r-9)(5 r-3)$ and write the result in standard form.

Studdy Solution

STEP 1

Assumptions
1. We are multiplying two binomials: $(7r - 9)$ and $(5r - 3)$ .
2. Standard form for a polynomial is written with the terms in descending order of their degrees.

STEP 2

To multiply two binomials, we will use the distributive property (also known as the FOIL method, which stands for First, Outer, Inner, Last), which states that each term in the first binomial must be multiplied by each term in the second binomial.

STEP 3

Multiply the first terms of each binomial (First).
$7r \times 5r = 35r^2$

STEP 4

Multiply the outer terms of the binomials (Outer).
$7r \times -3 = -21r$

STEP 5

Multiply the inner terms of the binomials (Inner).
$-9 \times 5r = -45r$

STEP 6

Multiply the last terms of each binomial (Last).
$-9 \times -3 = 27$

STEP 7

Combine the results from steps 3, 4, 5, and 6 to form a single expression.
$35r^2 - 21r - 45r + 27$

STEP 8

Combine like terms. In this case, combine the terms involving $r$ .
$35r^2 - (21r + 45r) + 27$

STEP 9

Perform the addition/subtraction of the like terms.
$35r^2 - 66r + 27$

STEP 10

Write the final expression in standard form, which is already achieved since the terms are in descending order of their degrees.
$35r^2 - 66r + 27$
The product of the binomials in standard form is $35r^2 - 66r + 27$ .

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