Question Express $(x-1)(x-9)$ as a trinomial.

Studdy Solution

STEP 1

Assumptions
1. We are given the expression $(x-1)(x-9)$ .
2. We need to expand this expression into a trinomial, which is a polynomial with three terms.

STEP 2

To expand the given expression, we will use the distributive property (also known as the FOIL method for binomials), which states that for any numbers $a$ , $b$ , $c$ , and $d$ ,
$(a + b)(c + d) = ac + ad + bc + bd$

STEP 3

Identify the terms in the given expression that will be multiplied together:
$(x - 1)(x - 9)$
Here, $a = x$ , $b = -1$ , $c = x$ , and $d = -9$ .

STEP 4

Multiply the first terms of each binomial together:
$ac = x \cdot x = x^2$

STEP 5

Multiply the outer terms of each binomial together:
$ad = x \cdot (-9) = -9x$

STEP 6

Multiply the inner terms of each binomial together:
$bc = (-1) \cdot x = -x$

STEP 7

Multiply the last terms of each binomial together:
$bd = (-1) \cdot (-9) = 9$

STEP 8

Combine all the products from steps 4 to 7 to form the expanded expression:
$x^2 - 9x - x + 9$

STEP 9

Combine like terms in the expanded expression. Here, the like terms are $-9x$ and $-x$ .
$x^2 - 9x - x + 9 = x^2 - (9x + x) + 9$

STEP 10

Simplify the like terms:
$x^2 - (9x + x) + 9 = x^2 - 10x + 9$

STEP 11

The expression $(x-1)(x-9)$ has been expanded into a trinomial:
$x^2 - 10x + 9$
This is the final result.

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