HSPT Math : How to simplify expressions

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #1 : How To Simplify Expressions

You are given that  are whole numbers.

Which of the following is true of   if  and  are both odd?

 

Possible Answers:

None of the other statements are true.

 is always odd.

 is always even.

 is always odd if  is odd, and always even if  is even.

 is always odd if  is even, and always even if  is odd.

Correct answer:

 is always odd if  is even, and always even if  is odd.

Explanation:

If  is odd, then  is odd, since the product of two odd whole numbers must be odd. When the odd number  is added, the result, , is even, since the sum of two odd numbers must be even.

If  is even, then  is even, since the product of an odd number and an even number must be even. When the odd number  is added, the result, , is odd, since the sum of an odd number and an even number must be odd.

Example Question #1 : How To Simplify Expressions

Simplify the expression:

Possible Answers:

Correct answer:

Explanation:

Combine all the like terms.

The  terms can be combined together, which gives you .

When you combine the  terms together, you get .

There is only one  term so it doesn't get combined with anything. Put them all together and you get 

.

Example Question #2 : How To Simplify Expressions

Simplify the following expression:

 \dpi{100} \small 2(4x-3x)-6t+5x

Possible Answers:

\dpi{100} \small 1x-6t+5

\dpi{100} \small 7x-6t

\dpi{100} \small 6t-7x

\dpi{100} \small 6x+11x

\dpi{100} \small 14x - 11xt

Correct answer:

\dpi{100} \small 7x-6t

Explanation:

\dpi{100} \small 2(4x-3x)-6t+5x

First distribute the 2:    \dpi{100} \small 8x-6x-6t+5x

Combine the like terms:      \dpi{100} \small 7x-6t

Example Question #571 : Problem Solving

Simplify the expression:

Possible Answers:

2x + 1

2x

x + 1

x

x+ 2x + 1

Correct answer:

x + 1

Explanation:

Factor out a (2x) from the denominator, which cancels with (2x) from the numerator. Then factor the numerator, which becomes (+ 1)(+ 1), of which one of them cancels and you're left with (+ 1).

Example Question #2 : How To Simplify An Expression

Simplify the following expression: x3 - 4(x2 + 3) + 15

Possible Answers:

x5 + 3

x3 – 3x2 + 15

x3 – 4x2 + 3

x3 – 12x2 + 15

Correct answer:

x3 – 4x2 + 3

Explanation:

To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x2 and -4 by 3.

x3 - 4x2 -12 + 15

You can then add -12 and 15, which equals 3.

You now have x3 - 4x2 + 3 and are finished. Just a reminder that x3 and 4x2 are not like terms as the x’s have different exponents.

Example Question #3 : How To Simplify Expressions

Simplify the following expression:

2x(x2 + 4ax – 3a2) – 4a2(4x + 3a)

Possible Answers:

–12a3 – 14a2x + 2x3

–12a– 22a2x + 8ax2 + 2x3

–12a– 14ax2 + 2x3

12a– 22a2x + 8ax2 + 2x3

12a– 16a2x + 8ax2 + 2x3

Correct answer:

–12a– 22a2x + 8ax2 + 2x3

Explanation:

Begin by distributing each part:

2x(x2 + 4ax – 3a2) = 2x * x2 + 2x * 4ax – 2x * 3a2 = 2x3 + 8ax2 – 6a2x

The second:

–4a2(4x + 3a) = –16a2x – 12a3

Now, combine these:

2x3 + 8ax2 – 6a2x – 16a2x – 12a3

The only common terms are those with a2x; therefore, this reduces to

2x3 + 8ax2 – 22a2x – 12a3

This is the same as the given answer:

–12a– 22a2x + 8ax2 + 2x3

Example Question #3 : How To Simplify Expressions

Which of the following does not simplify to ?

Possible Answers:

All of these simplify to

Correct answer:

Explanation:

5x – (6x – 2x) = 5x – (4x) = x

(x – 1)(x + 2) - x2 + 2 = x2 + x – 2 – x2 + 2 = x

x(4x)/(4x) = x

(3 – 3)x = 0x = 0

Example Question #5 : How To Simplify Expressions

Simplify:  

Possible Answers:

Correct answer:

Explanation:

In order to simplify this expression, distribute and multiply the outer term with the two inner terms.

Example Question #3 : How To Simplify Expressions

Simplify:  

Possible Answers:

Correct answer:

Explanation:

When the same bases are multiplied, their exponents can be added.  Similarly, when the bases are divided, their exponents can be subtracted.  Apply this rule for the given problem.

Example Question #5 : How To Simplify Expressions

Simplify:  

Possible Answers:

Correct answer:

Explanation:

To simplify this expression, reduce the term inside the parenthesis. 

Rewrite the negative exponent as a fraction.

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