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HSPT Math : How to simplify expressions

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Example Question #1 : How To Simplify Expressions

You are given that A,B,C are whole numbers.

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

Possible Answers:

AB +C is always odd.

AB +C is always odd if is even, and always even if is odd.

AB +C is always odd if is odd, and always even if is even.

None of the other statements are true.

AB +C is always even.

Correct answer:

AB +C 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, AB +C , 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, AB +C , is odd, since the sum of an odd number and an even number must be odd.

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Example Question #1 : How To Simplify Expressions

Simplify the expression:

3x^2+9x+10x^2+5y+(-11x)

Possible Answers:

13x^2+2x-5y

15x^2+5y

13x^2-2x+5y

11x^2+5y

Correct answer:

13x^2-2x+5y

Explanation:

Combine all the like terms.

The x^2 terms can be combined together, which gives you 13x^2 .

When you combine the terms together, you get -2x .

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

13x^2-2x+5y .

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Example Question #1 : How To Simplify Expressions

Simplify the following expression:

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

Possible Answers:

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

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

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

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

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

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

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Example Question #1 : How To Simplify Expressions

Simplify the expression:

$\frac{(x^2+2x+1)(2x)}{2x^2+2x}$

Possible Answers:

x²+ 2x + 1

x + 1

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 (x + 1)(x + 1), of which one of them cancels and you're left with (x + 1).

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Example Question #1 : How To Simplify Expressions

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

Possible Answers:

x^3-4x^2+3

x^5+3

x^3-4x^2+3

x^3-12x^2+15

x^3-3x^2+15

x^3-12x^2+15

Correct answer:

x^3-4x^2+3

Explanation:

To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x²and -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 4x²are not like terms as the x’s have different exponents.

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Example Question #11 : How To Simplify An Expression

Simplify the following expression:

2x(x² + 4ax – 3a²) – 4a²(4x + 3a)

Possible Answers:

–12a^3 – 14a²x + 2x³

–12a³– 22a²x + 8ax² + 2x³

12a³– 16a²x + 8ax² + 2x³

–12a³– 14ax² + 2x³

12a³– 22a²x + 8ax² + 2x³

Correct answer:

–12a³– 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:

–12a³– 22a²x + 8ax² + 2x³

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Example Question #7 : How To Simplify Expressions

Which of the following does not simplify to ?

Possible Answers:

$\frac{x(4x)}{4x}$

(3-3)x

All of these simplify to

(x - 1)(x + 2) - x^2 + 2

5x-(6x-2x)

Correct answer:

(3-3)x

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

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Example Question #2 : How To Simplify Expressions

Simplify: x^5(x^2+1)

Possible Answers:

x^7 + 1

x^7 + x^5

$x^{10} + 1$

x^7 + x

$x^{10} + x^5$

Correct answer:

x^7 + x^5

Explanation:

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

x^5(x^2+1) = x^5(x^2)+x^5(1) = x^7 + x^5

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Example Question #3 : How To Simplify Expressions

Simplify: $\frac{c^2 e}{c^{-2}e^{-3}}$

Possible Answers:

c^4e^4

$\frac{1}{e^2}$

$\frac{c^2}{e^2}$

c^4e^3

$\frac{1}{e^3}$

Correct answer:

c^4e^4

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.

$\frac{c^2 e}{c^{-2}e^{-3}}=c^{2-(-2)}e^{1-(-3)} = c^4e^4$

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Example Question #3 : How To Simplify Expressions

Simplify: $\left (\frac{3}{12} \right )^{-1}$

Possible Answers:

$\frac{1}{9}$

$\frac{1}{4}$

Correct answer:

Explanation:

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

$\left (\frac{3}{12} \right )^{-1}=\left (\frac{1}{4} \right )^{-1}$

Rewrite the negative exponent as a fraction.

$\left (\frac{1}{4} \right )^{-1} = \frac{1}{\left (\frac{1}{4} \right )^{1}} =4$

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HSPT Math : How to simplify expressions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : How To Simplify Expressions

Example Question #1 : How To Simplify Expressions

Example Question #1 : How To Simplify Expressions

Example Question #1 : How To Simplify Expressions

Example Question #1 : How To Simplify Expressions

Example Question #11 : How To Simplify An Expression

Example Question #7 : How To Simplify Expressions

Example Question #2 : How To Simplify Expressions

Example Question #3 : How To Simplify Expressions

Example Question #3 : How To Simplify Expressions

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