QuestionFind the equivalent expression for $-2 x^{2}+8 x-9+4 x+7 x^{2}+2$ . Options: A. $5 x^{2}+12 x-7$ , B. $-5 x^{2}+4 x+11$ , C. $-9 x^{2}-12 x+11$ , D. $-9 x^{2}+4 x-7$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $- x^{}+8 x-9+4 x+7 x^{}+$ . We are asked to find an equivalent expression from the options A, B, C, and D.

STEP 2

First, we need to simplify the given expression by combining like terms. Like terms are terms that have the same variables and powers. The coefficients of like terms can be combined.

STEP 3

Combine the $x^{2}$ terms.
$-2 x^{2} +7 x^{2}$

STEP 4

Calculate the combined $x^{2}$ term.
$-2 x^{2} +7 x^{2} = x^{2}$

STEP 5

Next, combine the $x$ terms.
$8 x +4 x$

STEP 6

Calculate the combined $x$ term.
$8 x +4 x =12 x$

STEP 7

Finally, combine the constant terms.
$-9 +2$

STEP 8

Calculate the combined constant term.
$- +2 = -7$

STEP 9

Now, put the combined terms together to form the simplified expression.
$5 x^{2} +12 x -7$

STEP 10

Compare the simplified expression with the options A, B, C, and D. The equivalent expression is option A.
$5 x^{2} +12 x -7$ Therefore, the expression equivalent to the given expression is $5 x^{2} +12 x -7$ .

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QuestionFind the equivalent expression for $-2 x^{2}+8 x-9+4 x+7 x^{2}+2$ . Options: A. $5 x^{2}+12 x-7$ , B. $-5 x^{2}+4 x+11$ , C. $-9 x^{2}-12 x+11$ , D. $-9 x^{2}+4 x-7$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $- x^{}+8 x-9+4 x+7 x^{}+$ . We are asked to find an equivalent expression from the options A, B, C, and D.

STEP 2

First, we need to simplify the given expression by combining like terms. Like terms are terms that have the same variables and powers. The coefficients of like terms can be combined.

STEP 3

Combine the $x^{2}$ terms.
$-2 x^{2} +7 x^{2}$

STEP 4

Calculate the combined $x^{2}$ term.
$-2 x^{2} +7 x^{2} = x^{2}$

STEP 5

Next, combine the $x$ terms.
$8 x +4 x$

STEP 6

Calculate the combined $x$ term.
$8 x +4 x =12 x$

STEP 7

Finally, combine the constant terms.
$-9 +2$

STEP 8

Calculate the combined constant term.
$- +2 = -7$

STEP 9

Now, put the combined terms together to form the simplified expression.
$5 x^{2} +12 x -7$

STEP 10

Compare the simplified expression with the options A, B, C, and D. The equivalent expression is option A.
$5 x^{2} +12 x -7$ Therefore, the expression equivalent to the given expression is $5 x^{2} +12 x -7$ .

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Studdy Solution

STEP 1

Assumptions1. We are given the expression −x+8x−9+4x+7x+- x^{}+8 x-9+4 x+7 x^{}+−x+8x−9+4x+7x+ . We are asked to find an equivalent expression from the options A, B, C, and D.

STEP 2

First, we need to simplify the given expression by combining like terms. Like terms are terms that have the same variables and powers. The coefficients of like terms can be combined.

STEP 3

Combine the x2x^{2}x2 terms.−2x2+7x2-2 x^{2} +7 x^{2}−2x2+7x2

STEP 4

Calculate the combined x2x^{2}x2 term.−2x2+7x2=x2-2 x^{2} +7 x^{2} = x^{2}−2x2+7x2=x2

STEP 5

Next, combine the xxx terms.8x+4x8 x +4 x8x+4x

STEP 6

Calculate the combined xxx term.8x+4x=12x8 x +4 x =12 x8x+4x=12x

STEP 7

Finally, combine the constant terms.−9+2-9 +2−9+2

STEP 8

Calculate the combined constant term.−+2=−7- +2 = -7−+2=−7

STEP 9

Now, put the combined terms together to form the simplified expression.5x2+12x−75 x^{2} +12 x -75x2+12x−7

STEP 10

Compare the simplified expression with the options A, B, C, and D. The equivalent expression is option A.5x2+12x−75 x^{2} +12 x -75x2+12x−7Therefore, the expression equivalent to the given expression is 5x2+12x−75 x^{2} +12 x -75x2+12x−7.

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Assumptions1. We are given the expression $- x^{}+8 x-9+4 x+7 x^{}+$ . We are asked to find an equivalent expression from the options A, B, C, and D.

Combine the $x^{2}$ terms.
$-2 x^{2} +7 x^{2}$

Calculate the combined $x^{2}$ term.
$-2 x^{2} +7 x^{2} = x^{2}$

Next, combine the $x$ terms.
$8 x +4 x$

Calculate the combined $x$ term.
$8 x +4 x =12 x$

Finally, combine the constant terms.
$-9 +2$

Calculate the combined constant term.
$- +2 = -7$

Now, put the combined terms together to form the simplified expression.
$5 x^{2} +12 x -7$

Compare the simplified expression with the options A, B, C, and D. The equivalent expression is option A.
$5 x^{2} +12 x -7$ Therefore, the expression equivalent to the given expression is $5 x^{2} +12 x -7$ .