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ISEE Middle Level Math : Algebraic Concepts

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Example Questions

Example Question #61 : Algebraic Concepts

Simplify the following expression:

2x*5y

Possible Answers:

10x*10y

7x*7y

The expression is already reduced.

10x+10y

10xy

Correct answer:

10xy

Explanation:

When you multiple variables, the constants will be multiplied together and the variables will be combined.

So that means that

2*5=10

and

x*y=xy

so that leaves us with a final answer of

10xy .

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Example Question #62 : Variables

Simplify the following expression:

(4b^2cl^6)(2bc^2l^3)

Possible Answers:

8b^3c^3l^9

$8b^2c^2l^{18}$

8b^4c^4l^9

6b^3c^3l^9

Correct answer:

8b^3c^3l^9

Explanation:

Simplify the following expression:

(4b^2cl^6)(2bc^2l^3)

We can simplify this by combining like terms. We need to multiply the two pieces in parentheses.

We can only combine variables with the same base.

To multiply variables we must add their exponents.

The integers (whole numbers) can be combined via standard multiplication.

So, we should get the following:

(4b^2cl^6)(2bc^2l^3)=8b^3c^3l^9

So our answer is:

8b^3c^3l^9

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Example Question #62 : Variables

Simplify the following expression:

6y (3y-2)

Possible Answers:

$18y^{2} + 12y$

$18y^{2} - 12$

$18y-12y^{2}$

$18y^{2} - 12y$

Correct answer:

$18y^{2} - 12y$

Explanation:

To solve 6y (3y-2) distribute the to each term in the parenthesis. Remember: When multiplying variables add the exponents.

$6y \times 3y = 18y^{^{2}}$

$6y\times-2 = -12y$

Rewrite:

$18y^{2} - 12y$

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Example Question #63 : Variables

$15t \times 3t^{4} =$

Possible Answers:

$45t^{5}$

$45t^{4}$

$18t^{5}$

$12t^{4}$

Correct answer:

$45t^{5}$

Explanation:

$15t\times3t^{4} =$

Multiply the coefficients of the variable

$15 \times 3 = 45$

Then multiply the variables by adding the exponents:

$t \times 3t^{4} = t^{1+4} = t^{5}$

$45t^{5}$ is the correct answer.

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Example Question #64 : Variables

$-4x (-2x^{2} +3y -4) =$

Possible Answers:

$8x^{3} +12xy -16x$

$-8x^{3} -12xy + 16y$

$8x^{3} -12xy +16x$

$8x^{2} -12xy +16x$

Correct answer:

$8x^{3} -12xy +16x$

Explanation:

First distribute the -4x to all terms in the parenthesis.

$(-4x \times -2x^{2}) + (-4x \times 3y) + (-4x \times -4)$

$(-4x \times -2x^{2}) = 8x ^{1+2} = 8x^{3}$ (When multiplying variables with exponents, the exponents are added together).

$(-4x \times 3y) = -4\times 3 \times x\times y = -12xy$

-4x (-4) = 16x

$8x^{3} -12xy + 16x$

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Example Question #65 : Variables

$(-6x^{4}y^{2}) \times (-3x^{2}y^{2})=$

Possible Answers:

$18x^{6}y^{4}$

$-18x^{6}y^{4}$

$18x^{8}y^{4}$

$-9x^{6}y^{4}$

Correct answer:

$18x^{6}y^{4}$

Explanation:

To solve $(-6x^{4}y^{2}) \times(-3x^{2}y^{2})$

Separate the parts of the terms. Multiply the coefficients:

$-6 \times - 3 = 18$

Multiply the terms with as the variable. When multiplying, the exponents get added.

$x^{4}\times x^{2} = x^{4+2} = x^{6}$

Multiply the terms with as the variable. When multiplying, the exponents get added.

$y^{2}\times y^{2} = y^{2+2} = y^{4}$

Put it all together:

$18x^{6}y^{4}$

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Example Question #66 : Variables

The length of a rectangle is and the width is 9{y}. What is the area of this rectangle?

Possible Answers:

13y

36y

26y

$36y^{2}$

Correct answer:

$36y^{2}$

Explanation:

The formula for the Area of a rectangle is length times width or l x w. Multiply the length which is times the width which is 9y.

First multiply

$4 \times 9 =36$

Then multiply the variables; add the exponents:

$y\timesy = y^{1+1} = y^{2}$

Area or A of the rectangle is

$36y^{2}$

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Example Question #68 : Variables

The length of a rectangular prism is centimeters. The width is centimeters. The height is centimeters. Find the volume of this rectangular prism.

Possible Answers:

$9x^{3}centimeters^{3}$

$240x^{3} centimeters^{3}$

$240 centimeters^{3}$

$19x^{3} centimeters ^{3}$

Correct answer:

$240x^{3} centimeters^{3}$

Explanation:

The volume of a rectangular prism is determined by using the formula

V = length x width x height

$8 \times 6\times 5 = 240$

$x \ast x \ast x = x^{1+1+1} =x^{3}$

$240x^{3} centimeters^{3}$

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Example Question #67 : Variables

Multiply the following:

$x \cdot 3x$

Possible Answers:

x^2

3x^2

Correct answer:

3x^2

Explanation:

When multiplying variables, we multiply them together just like we would integers. We have

$x \cdot 3x$

The first term isn't showing a coefficient, so it is automatically 1. So,

$1x \cdot 3x$

Now, we will multiply the coefficients together, then we multiply the variables together.

So, we get

$1x \cdot 3x = (1 \cdot 3)(x \cdot x) = 3x^2$

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Example Question #68 : Variables

Simplify the following expression:

$9x^3t^7*4x^5t^{12}$

Possible Answers:

$9x^8t^{19}$

$36x^8t^{19}$

$13x^8t^{19}$

$36x^8t^{84}$

Correct answer:

$36x^8t^{19}$

Explanation:

Simplify the following expression:

$9x^3t^7*4x^5t^{12}$

Let's begin by rewriting the expression with similar terms next to each other.

$(9*4)(x^3*x^5)(t^7*t^{12})$

Next, multiply the terms out.

Our first pair of terms is just like regular multiplication.

For the next two terms, we need to add the exponents.

In doing so, we get:

$36x^8t^{19}$

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ISEE Middle Level Math : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #61 : Algebraic Concepts

Example Question #62 : Variables

Example Question #62 : Variables

Example Question #63 : Variables

Example Question #64 : Variables

Example Question #65 : Variables

Example Question #66 : Variables

Example Question #68 : Variables

Example Question #67 : Variables

Example Question #68 : Variables

All ISEE Middle Level Math Resources

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