Video Tutorial Captions: Using the Distributive Property to Evaluate Expressions 11

The distributive property allows you to multiply a factor across multiple terms of an expression.

In this video we will look at the case where a is negative, b is positive, the coefficient of x is negative, and the expression in parentheses involves subtraction.

In this video we will look at the case where a is negative, b is positive, the coefficient of x is negative, and the expression in parentheses involves subtraction.

Let's start with an example.

A number is multiplied by -1, the product is decreased by 8, and the difference is multiplied by -5.

Use the distributive property to write the expression.

Evaluate the expression for x = 3.

This is an example of converting words into an algebraic expression.

Let's start with this part, "A number is multiplied by -1, the product is decreased by 8."

Let's start with this part, "A number is multiplied by -1, the product is decreased by 8."

Since we don't know which number, we designate it as -x.

This number is decreased by 8, so we write -x - 8.

This difference, or the entire expression, is multiplied by -5, so we enclose the expression in parentheses and multiply the whole expression by -5, as shown here.

This difference, or the entire expression, is multiplied by -5, so we enclose the expression in parentheses and multiply the whole expression by -5, as shown here.

This is the mathematical equivalent of this verbal expression.

We now distribute the -5 to both terms, as shown here.

The product of these two negative terms is positive, and the negative sign here changes subtraction to addition.

The product of these two negative terms is positive, and the negative sign here changes subtraction to addition.

We get 5x + 40.

We evaluate this expression for x = 3, as shown here.

We get 15 + 40, which is 55.

Let's look at another example.

A number is multiplied by -1, the product is decreased by 15, and the difference is multiplied by -12.

Use the distributive property to write the expression.

Evaluate the expression for x = -7.

This is an example of converting words into an algebraic expression.

Let's start with this part, "A number is multiplied by -1, the product is decreased by 15."

Since we don't know which number, we designate it as -x.

This number is decreased by 15, so we write -x - 15.

This difference, or the entire expression, is multiplied by -12, so we enclose the expression in parentheses and multiply the whole expression by -12, as shown here.

This difference, or the entire expression, is multiplied by -12, so we enclose the expression in parentheses and multiply the whole expression by -12, as shown here.

This is the mathematical equivalent of this verbal expression.

We now distribute the -12 to both terms, as shown here.

The product of these two negative terms is positive, and the negative sign here changes subtraction to addition.

The product of these two negative terms is positive, and the negative sign here changes subtraction to addition.

We get 12x + 180.

We evaluate this expression for x = -7, as shown here.

We get -84 + 180, which is 96.

Let's look at a final example.

A number is multiplied by -1, the product is decreased by 28, and the difference is multiplied by -32.

Use the distributive property to write the expression.

Evaluate the expression for x = -1.

This is an example of converting words into an algebraic expression.

Let's start with this part, "A number is multiplied by -1, the product is decreased by 28."

Let's start with this part, "A number is multiplied by -1, the product is decreased by 28."

Since we don't know which number, we designate it as -x.

This number is decreased by 28, so we write -x - 28.

This difference, or the entire expression, is multiplied by -32, so we enclose the expression in parentheses and multiply the whole expression by -32, as shown here.

This difference, or the entire expression, is multiplied by -32, so we enclose the expression in parentheses and multiply the whole expression by -32, as shown here.

This is the mathematical equivalent of this verbal expression.

We now distribute the -32 to both terms, as shown here.

The product of these two negative terms is positive, and the negative sign here changes subtraction to addition.

The product of these two negative terms is positive, and the negative sign here changes subtraction to addition.

We get 32x + 896.

We evaluate this expression for x = -1, as shown here.

We get -32 + 896, or 864.