How to subtract exponential variables - ISEE Upper Level Quantitative Reasoning

Card 0 of 36

Question

Simplify the expression:

Answer

Group, then collect like terms:

$=\left ( 7 + 9 \right $)x^{3}$ - $5x^{2}$$

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Question

Simplify:

Answer

$=\frac{8xy}{xy}$ = 8$

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Question

Assume that $x \neq 0$ . Which of the following expressions is equivalent to:

$$\frac{\left(x+1 \right) ^{3}$ - \left ( $x^{3 }$ + 1\right ) $}{x^{2}$}$ ?

Answer

$$\frac{\left(x+1 \right) ^{3}$ - \left ( $x^{3 }$ + 1\right ) $}{x^{2}$}$

$= $\frac{\left $(x^{3}$$ $+3x^{2}$ + 3x + 1 ) - \left( $x^{3 }$ + 1\right) $}{x^{2}$}$

$= $$\frac{x^{3}$$ $-x^{3}$ $+3x^{2}$ + 3x + $1-1}{x^{2}$}$

$= $$\frac{3x^{2}$$ + 3x $}{x^{2}$}$

$= $$\frac{3x^{2}$$ $}{x^{2}$} + $\frac{ 3x $}{x^{2}$$}$

$=3 + $\frac{ 3 }{x}$$

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Question

If $x,y\neq 0$ , simplify:

Answer

$=\frac{4xy}{xy}$=4$

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Question

If $x\neq 0$ , simplify:

Answer

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Question

If $x\neq 0$ , simplify:

Answer

$=\frac{2(1-x)}{x-1}$$

$=\frac{2(1-x)}{-1(1-x)}$$

$=\frac{2}{-1}$=-2$

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Question

If $x,y\neq 0$ , simplify:

Answer

$=\frac{2xy}{xy}$=2$

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Question

If $x\neq 0$ , simplify:

Answer

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Question

Simplify the following expression:

Answer

Simplify the following expression:

We can treat this basically as a regular subtraction problem.

We want to subtract our coefficients, while leaving the exponents the same.

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Question

Simplify the expression:

Answer

Group, then collect like terms:

$=\left ( 7 + 9 \right $)x^{3}$ - $5x^{2}$$

Compare your answer with the correct one above

Question

Simplify:

Answer

$=\frac{8xy}{xy}$ = 8$

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Question

Assume that $x \neq 0$ . Which of the following expressions is equivalent to:

$$\frac{\left(x+1 \right) ^{3}$ - \left ( $x^{3 }$ + 1\right ) $}{x^{2}$}$ ?

Answer

$$\frac{\left(x+1 \right) ^{3}$ - \left ( $x^{3 }$ + 1\right ) $}{x^{2}$}$

$= $\frac{\left $(x^{3}$$ $+3x^{2}$ + 3x + 1 ) - \left( $x^{3 }$ + 1\right) $}{x^{2}$}$

$= $$\frac{x^{3}$$ $-x^{3}$ $+3x^{2}$ + 3x + $1-1}{x^{2}$}$

$= $$\frac{3x^{2}$$ + 3x $}{x^{2}$}$

$= $$\frac{3x^{2}$$ $}{x^{2}$} + $\frac{ 3x $}{x^{2}$$}$

$=3 + $\frac{ 3 }{x}$$

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Question

If $x,y\neq 0$ , simplify:

Answer

$=\frac{4xy}{xy}$=4$

Compare your answer with the correct one above

Question

If $x\neq 0$ , simplify:

Answer

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Question

If $x\neq 0$ , simplify:

Answer

$=\frac{2(1-x)}{x-1}$$

$=\frac{2(1-x)}{-1(1-x)}$$

$=\frac{2}{-1}$=-2$

Compare your answer with the correct one above

Question

If $x,y\neq 0$ , simplify:

Answer

$=\frac{2xy}{xy}$=2$

Compare your answer with the correct one above

Question

If $x\neq 0$ , simplify:

Answer

Compare your answer with the correct one above

Question

Simplify the following expression:

Answer

Simplify the following expression:

We can treat this basically as a regular subtraction problem.

We want to subtract our coefficients, while leaving the exponents the same.

Compare your answer with the correct one above

Question

Simplify the expression:

Answer

Group, then collect like terms:

$=\left ( 7 + 9 \right $)x^{3}$ - $5x^{2}$$

Compare your answer with the correct one above

Question

Simplify:

Answer

$=\frac{8xy}{xy}$ = 8$

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