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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #53 : How To Simplify An Expression

Simplify the expression:

$2x^{4}+3x^{3}-x^{2}+5x+6-(2x^{3}-2x^{2}+4x+2)$ $\displaystyle 2x^{4}+3x^{3}-x^{2}+5x+6-(2x^{3}-2x^{2}+4x+2)$

Possible Answers:

$2x^{4}+x^{3}+x^{2}+9x+8$ $\displaystyle 2x^{4}+x^{3}+x^{2}+9x+8$

$2x^{4}+x^{3}+x^{2}+x+4$ $\displaystyle 2x^{4}+x^{3}+x^{2}+x+4$

$2x^{4}+3x^{3}+x^{2}+x+4$ $\displaystyle 2x^{4}+3x^{3}+x^{2}+x+4$

$2x^{4}-x^{3}+x^{2}+x+4$ $\displaystyle 2x^{4}-x^{3}+x^{2}+x+4$

Correct answer:

$2x^{4}+x^{3}+x^{2}+x+4$ $\displaystyle 2x^{4}+x^{3}+x^{2}+x+4$

Explanation:

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. However, because this problem has a minus sign, it first needs to be distributed. That would look as follows:

$2x^{4}+3x^{3}-x^{2}+5x+6-(2x^{3}-2x^{2}+4x+2)$ $\displaystyle 2x^{4}+3x^{3}-x^{2}+5x+6-(2x^{3}-2x^{2}+4x+2)$

$2x^{4}+3x^{3}-x^{2}+5x+6-2x^{3}+2x^{2}-4x-2$ $\displaystyle 2x^{4}+3x^{3}-x^{2}+5x+6-2x^{3}+2x^{2}-4x-2$

$2x^{4}+3x^{3}-2x^{3}+2x^{2}-x^{2}+5x-4x-2+6$ $\displaystyle 2x^{4}+3x^{3}-2x^{3}+2x^{2}-x^{2}+5x-4x-2+6$

$2x^{4}+x^{3}+x^{2}+x+4$ $\displaystyle 2x^{4}+x^{3}+x^{2}+x+4$

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Example Question #812 : Algebra

Simplify the expression:

$3x^{2}+2x-7+x^{2}+3x+6$ $\displaystyle 3x^{2}+2x-7+x^{2}+3x+6$

Possible Answers:

$x^{2}+5x+1$ $\displaystyle x^{2}+5x+1$

$4x^{2}+5x-1$ $\displaystyle 4x^{2}+5x-1$

$2x^{2}+5x-1$ $\displaystyle 2x^{2}+5x-1$

$4x^{2}+3x-12$ $\displaystyle 4x^{2}+3x-12$

Correct answer:

$4x^{2}+5x-1$ $\displaystyle 4x^{2}+5x-1$

Explanation:

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. That would look as follows:

$3x^{2}+2x-7+x^{2}+3x+6$ $\displaystyle 3x^{2}+2x-7+x^{2}+3x+6$

$3x^{2}+x^{2}+2x+3x-7+6$ $\displaystyle 3x^{2}+x^{2}+2x+3x-7+6$

$4x^{2}+5x-1$ $\displaystyle 4x^{2}+5x-1$

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Example Question #51 : Simplifying Expressions

Simplify the expression:

$x+7+x^{2}+3x-4$ $\displaystyle x+7+x^{2}+3x-4$

Possible Answers:

$x^{2}+4x+3$ $\displaystyle x^{2}+4x+3$

$x^{2}+2x-3$ $\displaystyle x^{2}+2x-3$

$2x^{2}+4x-3$ $\displaystyle 2x^{2}+4x-3$

$x^{2}-4x+3$ $\displaystyle x^{2}-4x+3$

Correct answer:

$x^{2}+4x+3$ $\displaystyle x^{2}+4x+3$

Explanation:

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. That would look as follows:

$x+7+x^{2}+3x-4$ $\displaystyle x+7+x^{2}+3x-4$

$x^{2}+x+3x+7-4$ $\displaystyle x^{2}+x+3x+7-4$

$x^{2}+4x+3$ $\displaystyle x^{2}+4x+3$

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Example Question #56 : How To Simplify An Expression

Simplify the expression:

$x^{3}-6x^{2}+3x-5-(-2x^{3}+4x^{2}+3x-4)$ $\displaystyle x^{3}-6x^{2}+3x-5-(-2x^{3}+4x^{2}+3x-4)$

Possible Answers:

$3x^{3}-10x^{2}-9$ $\displaystyle 3x^{3}-10x^{2}-9$

$3x^{3}-10x^{2}+6x-1$ $\displaystyle 3x^{3}-10x^{2}+6x-1$

$2x^{3}-10x^{2}-6x-1$ $\displaystyle 2x^{3}-10x^{2}-6x-1$

$3x^{3}-10x^{2}-1$ $\displaystyle 3x^{3}-10x^{2}-1$

Correct answer:

$3x^{3}-10x^{2}-1$ $\displaystyle 3x^{3}-10x^{2}-1$

Explanation:

$x^{3}-6x^{2}+3x-5-(-2x^{3}+4x^{2}+3x-4)$ $\displaystyle x^{3}-6x^{2}+3x-5-(-2x^{3}+4x^{2}+3x-4)$

$x^{3}-6x^{2}+3x-5+2x^{3}-4x^{2}-3x+4$ $\displaystyle x^{3}-6x^{2}+3x-5+2x^{3}-4x^{2}-3x+4$

$x^{3}+2x^{3}-6x^{2}-4x^{2}+3x-3x-5+4$ $\displaystyle x^{3}+2x^{3}-6x^{2}-4x^{2}+3x-3x-5+4$

$3x^{3}-10x^{2}-1$ $\displaystyle 3x^{3}-10x^{2}-1$

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Example Question #57 : How To Simplify An Expression

Simplify the expression:

$4x^{2}+4x-6-(2x^{2}-x-2)$ $\displaystyle 4x^{2}+4x-6-(2x^{2}-x-2)$

Possible Answers:

$x^{2}-5x-4$ $\displaystyle x^{2}-5x-4$

$2x^{2}+5x-4$ $\displaystyle 2x^{2}+5x-4$

$2x^{2}+2x-3$ $\displaystyle 2x^{2}+2x-3$

$2x^{2}+5x-8$ $\displaystyle 2x^{2}+5x-8$

Correct answer:

$2x^{2}+5x-4$ $\displaystyle 2x^{2}+5x-4$

Explanation:

$4x^{2}+4x-6-(2x^{2}-x-2)$ $\displaystyle 4x^{2}+4x-6-(2x^{2}-x-2)$

$4x^{2}+4x-6-2x^{2}+x+2$ $\displaystyle 4x^{2}+4x-6-2x^{2}+x+2$

$4x^{2}-2x^{2}+4x+x-6+2$ $\displaystyle 4x^{2}-2x^{2}+4x+x-6+2$

$2x^{2}+5x-4$ $\displaystyle 2x^{2}+5x-4$

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Example Question #58 : How To Simplify An Expression

Simplify the expression:

$4x^{2}+5x-7-(x^{2}+6x+2)$ $\displaystyle 4x^{2}+5x-7-(x^{2}+6x+2)$

Possible Answers:

$3x^{2}-x-12$ $\displaystyle 3x^{2}-x-12$

$3x^{2}-x-9$ $\displaystyle 3x^{2}-x-9$

$3x^{2}+x+9$ $\displaystyle 3x^{2}+x+9$

$2x^{2}-4x-9$ $\displaystyle 2x^{2}-4x-9$

Correct answer:

$3x^{2}-x-9$ $\displaystyle 3x^{2}-x-9$

Explanation:

$4x^{2}+5x-7-(x^{2}+6x+2)$ $\displaystyle 4x^{2}+5x-7-(x^{2}+6x+2)$

$4x^{2}+5x-7-x^{2}+6x-2$ $\displaystyle 4x^{2}+5x-7-x^{2}+6x-2$

$4x^{2}-x^{2}+5x-6x-7-2$ $\displaystyle 4x^{2}-x^{2}+5x-6x-7-2$

$3x^{2}-x-9$ $\displaystyle 3x^{2}-x-9$

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Example Question #51 : How To Simplify An Expression

Simplify the expression:

$x^{3}-3x^{2}+4x+3-(x^{3}-5x^{2}-3x+2)$ $\displaystyle x^{3}-3x^{2}+4x+3-(x^{3}-5x^{2}-3x+2)$

Possible Answers:

$2x^{3}+2x^{2}+7x+1$ $\displaystyle 2x^{3}+2x^{2}+7x+1$

$x^{3}+2x^{2}+7x+1$ $\displaystyle x^{3}+2x^{2}+7x+1$

$2x^{2}+7x-11$ $\displaystyle 2x^{2}+7x-11$

$2x^{2}+7x+1$ $\displaystyle 2x^{2}+7x+1$

Correct answer:

$2x^{2}+7x+1$ $\displaystyle 2x^{2}+7x+1$

Explanation:

$x^{3}-3x^{2}+4x+3-(x^{3}-5x^{2}-3x+2)$ $\displaystyle x^{3}-3x^{2}+4x+3-(x^{3}-5x^{2}-3x+2)$

$x^{3}-3x^{2}+4x+3-x^{3}+5x^{2}+3x-2$ $\displaystyle x^{3}-3x^{2}+4x+3-x^{3}+5x^{2}+3x-2$

$x^{3}-x^{3}-3x^{2}+5x^{2}+4x+3x+3-2$ $\displaystyle x^{3}-x^{3}-3x^{2}+5x^{2}+4x+3x+3-2$

$2x^{2}+7x+1$ $\displaystyle 2x^{2}+7x+1$

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Example Question #52 : Simplifying Expressions

Simplify the expression:

$3x^{4}-2x^{3}+x^{2}+6x-2+x^{4}+3x^{3}+4x^{2}-5x+4$ $\displaystyle 3x^{4}-2x^{3}+x^{2}+6x-2+x^{4}+3x^{3}+4x^{2}-5x+4$

Possible Answers:

$4x^{4}+x^{3}+5x^{2}+x+2$ $\displaystyle 4x^{4}+x^{3}+5x^{2}+x+2$

$x^{3}+5x^{2}+x+2$ $\displaystyle x^{3}+5x^{2}+x+2$

$4x^{4}+6x^{3}+5x^{2}+x+3$ $\displaystyle 4x^{4}+6x^{3}+5x^{2}+x+3$

$x^{4}+x^{3}+2x^{2}+x+2$ $\displaystyle x^{4}+x^{3}+2x^{2}+x+2$

Correct answer:

$4x^{4}+x^{3}+5x^{2}+x+2$ $\displaystyle 4x^{4}+x^{3}+5x^{2}+x+2$

Explanation:

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. That would look as follows:

$3x^{4}-2x^{3}+x^{2}+6x-2+x^{4}+3x^{3}+4x^{2}-5x+4$ $\displaystyle 3x^{4}-2x^{3}+x^{2}+6x-2+x^{4}+3x^{3}+4x^{2}-5x+4$

$3x^{4}+x^{4}-2x^{3}+3x^{3}+x^{2}+4x^{2}+6x-5x-2+4$ $\displaystyle 3x^{4}+x^{4}-2x^{3}+3x^{3}+x^{2}+4x^{2}+6x-5x-2+4$

$4x^{4}+x^{3}+5x^{2}+x+2$ $\displaystyle 4x^{4}+x^{3}+5x^{2}+x+2$

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Example Question #2591 : Sat Mathematics

Simplify the expression:

$-x^{2}+3x+7+2x^{2}+4x+2$ $\displaystyle -x^{2}+3x+7+2x^{2}+4x+2$

Possible Answers:

$x^{2}+7x+12$ $\displaystyle x^{2}+7x+12$

$2x^{2}+7x+9$ $\displaystyle 2x^{2}+7x+9$

$x^{2}+7x+9$ $\displaystyle x^{2}+7x+9$

$x^{2}+3x+2$ $\displaystyle x^{2}+3x+2$

Correct answer:

$x^{2}+7x+9$ $\displaystyle x^{2}+7x+9$

Explanation:

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. That would look as follows:

$-x^{2}+3x+7+2x^{2}+4x+2$ $\displaystyle -x^{2}+3x+7+2x^{2}+4x+2$

$2x^{2}-x^{2}+4x+3x+7+2$ $\displaystyle 2x^{2}-x^{2}+4x+3x+7+2$

$x^{2}+7x+9$ $\displaystyle x^{2}+7x+9$

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Example Question #62 : How To Simplify An Expression

Simplify the expression:

$4x-5+2x^{2}-3x+4$ $\displaystyle 4x-5+2x^{2}-3x+4$

Possible Answers:

$2x^{2}+3x-1$ $\displaystyle 2x^{2}+3x-1$

$2x^{2}+x+9$ $\displaystyle 2x^{2}+x+9$

$2x^{2}+x-1$ $\displaystyle 2x^{2}+x-1$

$x^{2}+x-12$ $\displaystyle x^{2}+x-12$

Correct answer:

$2x^{2}+x-1$ $\displaystyle 2x^{2}+x-1$

Explanation:

In order to simplify an expression, we rearrange it to put terms with the same base or type of variable together, then add or subtract accordingly. That would look as follows:

$4x-5+2x^{2}-3x+4$ $\displaystyle 4x-5+2x^{2}-3x+4$

$2x^{2}+4-3x-5+4$ $\displaystyle 2x^{2}+4-3x-5+4$

$2x^{2}+x-1$ $\displaystyle 2x^{2}+x-1$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #53 : How To Simplify An Expression

Example Question #812 : Algebra

Example Question #51 : Simplifying Expressions

Example Question #56 : How To Simplify An Expression

Example Question #57 : How To Simplify An Expression

Example Question #58 : How To Simplify An Expression

Example Question #51 : How To Simplify An Expression

Example Question #52 : Simplifying Expressions

Example Question #2591 : Sat Mathematics

Example Question #62 : How To Simplify An Expression

All SAT Math Resources

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