Algebra - HSPT Math

Card 0 of 20

Question

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

Answer

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.

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Question

Which of the following does not simplify to ?

Answer

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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Question

Simplify the following expression:

2x(x2 + 4ax – 3a2) – 4a2(4x + 3a)

Answer

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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Question

Simplify the expression:

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

Answer

Factor out a (2_x_) from the denominator, which cancels with (2_x_) 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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Question

Simplify the following expression:

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

Answer

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

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

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

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Question

You are given that are whole numbers.

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

Answer

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.

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Question

Simplify the expression:

Answer

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

.

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Question

Simplify:

Answer

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

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Question

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

Answer

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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Question

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

Answer

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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Question

Simplify the expression

Answer

To simplify this expression, combine like terms. In this expression, and are like terms. They are like terms because each term consists of a single variable,, and a numeric coefficient. Add the coefficients of these terms. Addition is the operation that you would use denoted by a plus sign next to the x.

and are also like terms. They are like terms because each term consists of a single variable, , and a numeric coefficient. These two like terms are separated by a subtraction sign, therefore subtraction is the operation you would use

Therefore, the correct answer is

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Question

Simplify the expression $3a^{2}b^{2} + 6ab^{2} + 7a^{2}b^{2} + 9ab^{2}$

Answer

To simplify this expression, combine like terms. In this expression, $3a^{2}b^{2}$ and $7a^{2}b^{2}$ are like terms. They are like terms because each term consists of a $a^{2}b^{2}$ , and a numeric coefficient. Add the coefficients of these terms. Addition is the operation that you would use denoted by a plus sign.

$3a^{2} b^{2} + 7a^{2}b^{2} = 10a^{2}b^{2}$

$6ab^{2}$ and $9ab^{2}$ are also like terms. They are like terms because each term consists of $ab^{2}$ and a numeric coefficient. These two like terms are separated by a addition sign, therefore addition is the operation you would use.

$6ab^{2} + 9ab^{2} = 15ab^{2}$

Therefore, the correct answer is

$10a^{2}b^{2} + 15ab^{2}$

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Question

Simplify the expression:

Answer

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

.

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Question

Suppose you know the values of , , and , and you want to evaluate the expression below.

$A + B^{2}\div C$

Which of the following is the first step you must complete?

Answer

Use the order of operations, PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

In our expression, there are no parentheses, so square first.

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Question

If you rewrite the phrase "the product of nine and a number added to the sum of six and twice the number" as an algebraic expression, then simplify the expression, the result is:

Answer

"The product of nine and a number" is . "Twice the number" is , and "The sum of six and twice the number" is .

"The product...added to the sum..." is ; simplify to get

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Question

Simplify the expression:

Answer

$= 9-3x + 4 \cdot x-4 \cdot 1$

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Question

Simplify:

Answer

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Question

$6^{3} \div (11-5)=$

Answer

First find the exponent value: $6^{3}=216$

Then find the value of $\left ( 11-5 \right )=6$

Finally, solve the entire expression with the known values: $216\div 6=36$

The answer is 36.

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Question

$3\frac{2}{5} \div 1 \frac{1}{5}=$

Answer

First convert each mixed number into and improper fraction

$\frac{17}{5} \div \frac{6}{5}$

Then convert the operation to multiplication and flip the second fraction

$\frac{17}{5} \ast \frac{5}{6}=$

Reduce where possible and multiply to solve:

$\frac{17}{6}=2\frac{5}{6}$

The answer is $2\frac{5}{6}$

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Question

Multiply:

Answer

Use the distributive property:

$4x(3x-2)=(4x\times3x)-(4x\times2)=12x^2-8x$

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