Question

Simplify 42+7a using the distributive property

Answer 1

Answer:

7(6 + a)

General Formulas and Concepts:

Algebra I

• Factoring

Step-by-step explanation:

Step 1: Define

42 + 7a

Step 2: Simplify

1. Factor out GCF (7):                                                                                               7(6 + a)

Answer 2

Hey there!

Note:

This expression is already simplified using the Distributive Property. So in order to simplify this expression, we need to factor.

Factoring is the opposite of distributing:

Distributing looks like so:

a(b+c)=ab+ac

So we have a term a and we distribute it by multiplying it times b and c; a, b, and c can be either constants or variables (constants are numbers, and variables are letters, or we can have both numbers and variables in a term - in that case, numbers are called coefficients)

That's why this property is called "The Distributive Property" because we take a term outside the parentheses and distribute it.

Factoring looks like so:

ab+ac=a(b+c)

Instead of multiplying times the common term, we divide by the common term.

And factoring is exactly what we should do here.

We have

$\hookrightarrow\sf{42+7a}$

What is the Greatest Common Factor? That's right, 7.

In order to factor it out, we should divide the entire binomial (a polynomial with 2 terms) by 7.

This is what we get:

$\hookrightarrow\sf{7(6+a)}$

Are we able to simplify this expression any further? No, because 6 and a aren't like terms.

Hope everything is clear.

Let me know if you have any questions!

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