Simplifying Expressions

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SAT Math › Simplifying Expressions

Questions 1 - 10
1

If 6 less than the product of 9 and a number is equal to 48, what is the number?

6

5

4

3

Explanation

Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.

2

If 6 less than the product of 9 and a number is equal to 48, what is the number?

6

5

4

3

Explanation

Write an equation for the written expression: 9x – 6 = 48. When we solve for x we get x = 6.

3

If x Sat_math_164_01 y = (5x - 4y)/y , find the value of y if 6 Sat_math_164_01 y = 2.

2

4

5

10

Explanation

If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 **-->**2y =30 -4y --> 6y =30 --> y=5. We could also work from the answers and substitute each answer in and solve.

4

If x Sat_math_164_01 y = (5x - 4y)/y , find the value of y if 6 Sat_math_164_01 y = 2.

2

4

5

10

Explanation

If we substitute 6 in for x in the given equation and set our answer to 2, we can solve for y algebraically. 30 minus 4y divided by y equals 2 **-->**2y =30 -4y --> 6y =30 --> y=5. We could also work from the answers and substitute each answer in and solve.

5

Simplify the expression:

Explanation

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. However, because this problem has a minus sign, it first needs to be distributed. That would look as follows:

6

Simplify the expression:

Explanation

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. However, because this problem has a minus sign, it first needs to be distributed. That would look as follows:

7

Given , simplify the following expression.

Explanation

Taking a look at the given expression, we can see that we have two fractions divided by one another. The first fraction in the numerator is , and the second fraction in the denominator is .

Remember that when we have a fraction divided by a fraction, that is the same thing as multiplying the numerator by the reciprocal of the denominator. To simplify, we will do just that.

.

To double check your answer, you can choose a numerical value for a and b and plug them into the expression.

8

Given , simplify the following expression.

Explanation

Taking a look at the given expression, we can see that we have two fractions divided by one another. The first fraction in the numerator is , and the second fraction in the denominator is .

Remember that when we have a fraction divided by a fraction, that is the same thing as multiplying the numerator by the reciprocal of the denominator. To simplify, we will do just that.

.

To double check your answer, you can choose a numerical value for a and b and plug them into the expression.

9

Evaluate: (2x + 4)(x2 – 2x + 4)

2x3 – 4x2 + 8x

2x3 – 8x2 + 16x + 16

2x3 + 16

2x3 + 8x2 – 16x – 16

4x2 + 16x + 16

Explanation

Multiply each term of the first factor by each term of the second factor and then combine like terms.

(2x + 4)(x2 – 2x + 4) = 2x3 – 4x2 + 8x + 4x2 – 8x + 16 = 2x3 + 16

10

Evaluate: (2x + 4)(x2 – 2x + 4)

2x3 – 4x2 + 8x

2x3 – 8x2 + 16x + 16

2x3 + 16

2x3 + 8x2 – 16x – 16

4x2 + 16x + 16

Explanation

Multiply each term of the first factor by each term of the second factor and then combine like terms.

(2x + 4)(x2 – 2x + 4) = 2x3 – 4x2 + 8x + 4x2 – 8x + 16 = 2x3 + 16

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