QuestionMultiply the polynomials and combine like terms: $(7x - 5)(x + 2)$ .

Studdy Solution

STEP 1

Assumptions1. We are given two polynomials $7x -5$ and $x +$ . . We need to multiply these polynomials using the distributive property.
3. The distributive property states that $a(b + c) = ab + ac$ .
4. We need to combine like terms after multiplication.

STEP 2

First, apply the distributive property to multiply the first term of the first polynomial ( $7x$ ) with each term in the second polynomial ( $x$ and $2$ ).
$7x \cdot (x +2) =7x \cdot x +7x \cdot2$

STEP 3

Perform the multiplication operations.
$7x \cdot x +7x \cdot2 =7x^2 +14x$

STEP 4

Next, apply the distributive property to multiply the second term of the first polynomial ( $-$ ) with each term in the second polynomial ( $x$ and $2$ ).
$- \cdot (x +2) = - \cdot x - \cdot2$

STEP 5

Perform the multiplication operations.
$-5 \cdot x -5 \cdot2 = -5x -10$

STEP 6

Combine the results from3 and5 to get the final result.
$x^2 +14x -5x -10$

STEP 7

Combine like terms to simplify the expression.
$7x^2 + (14x -5x) -10$

STEP 8

Perform the subtraction operation.
$7x^2 +x -10$ So, the result of multiplying the polynomials $7x -5$ and $x +2$ is $7x^2 +x -10$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms