QuestionSimplify the expression: $(9 x^{2}+9-3 x)-(4-6 x+8 x^{2})$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(9 x^{}+9-3 x\right)-\left(4-6 x+8 x^{}\right)$ . We need to simplify this expression by combining like terms

STEP 2

First, we need to get rid of the parentheses. According to the rules of algebra, when a minus sign precedes a parenthesis, we change the sign of each term inside the parenthesis.
$\left(9 x^{2}+9- x\right)-\left(4-6 x+8 x^{2}\right) =9 x^{2}+9- x -4 +6 x -8 x^{2}$

STEP 3

Next, we rearrange the terms so that like terms are together.
$9 x^{2}+9-3 x - +6 x -8 x^{2} =9 x^{2} -8 x^{2} -3 x +6 x +9 -$

STEP 4

Now, we combine the like terms.
$9 x^{2} -8 x^{2} -3 x +6 x +9 -4 = (9 -8) x^{2} + (-3 +6) x + (9 -4)$

STEP 5

Perform the operations inside the parentheses.
$(9 -8) x^{2} + (-3 +) x + (9 -4) =1 x^{2} +3 x +5$

STEP 6

Finally, we simplify the expression by removing the coefficient1 in front of $x^{2}$ .
$1 x^{2} +3 x +5 = x^{2} +3 x +5$ The simplified form of the given expression is $x^{2} +3 x +5$ .

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QuestionSimplify the expression: $(9 x^{2}+9-3 x)-(4-6 x+8 x^{2})$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(9 x^{}+9-3 x\right)-\left(4-6 x+8 x^{}\right)$ . We need to simplify this expression by combining like terms

STEP 2

First, we need to get rid of the parentheses. According to the rules of algebra, when a minus sign precedes a parenthesis, we change the sign of each term inside the parenthesis.
$\left(9 x^{2}+9- x\right)-\left(4-6 x+8 x^{2}\right) =9 x^{2}+9- x -4 +6 x -8 x^{2}$

STEP 3

Next, we rearrange the terms so that like terms are together.
$9 x^{2}+9-3 x - +6 x -8 x^{2} =9 x^{2} -8 x^{2} -3 x +6 x +9 -$

STEP 4

Now, we combine the like terms.
$9 x^{2} -8 x^{2} -3 x +6 x +9 -4 = (9 -8) x^{2} + (-3 +6) x + (9 -4)$

STEP 5

Perform the operations inside the parentheses.
$(9 -8) x^{2} + (-3 +) x + (9 -4) =1 x^{2} +3 x +5$

STEP 6

Finally, we simplify the expression by removing the coefficient1 in front of $x^{2}$ .
$1 x^{2} +3 x +5 = x^{2} +3 x +5$ The simplified form of the given expression is $x^{2} +3 x +5$ .

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QuestionSimplify the expression: (9x2+9−3x)−(4−6x+8x2)(9 x^{2}+9-3 x)-(4-6 x+8 x^{2})(9x2+9−3x)−(4−6x+8x2).

Studdy Solution

STEP 1

Assumptions1. We are given the expression (9x+9−3x)−(4−6x+8x)\left(9 x^{}+9-3 x\right)-\left(4-6 x+8 x^{}\right)(9x+9−3x)−(4−6x+8x). We need to simplify this expression by combining like terms

STEP 2

STEP 3

Next, we rearrange the terms so that like terms are together.9x2+9−3x−+6x−8x2=9x2−8x2−3x+6x+9−9 x^{2}+9-3 x - +6 x -8 x^{2} =9 x^{2} -8 x^{2} -3 x +6 x +9 -9x2+9−3x−+6x−8x2=9x2−8x2−3x+6x+9−

STEP 4

Now, we combine the like terms.9x2−8x2−3x+6x+9−4=(9−8)x2+(−3+6)x+(9−4)9 x^{2} -8 x^{2} -3 x +6 x +9 -4 = (9 -8) x^{2} + (-3 +6) x + (9 -4)9x2−8x2−3x+6x+9−4=(9−8)x2+(−3+6)x+(9−4)

STEP 5

Perform the operations inside the parentheses.(9−8)x2+(−3+)x+(9−4)=1x2+3x+5(9 -8) x^{2} + (-3 +) x + (9 -4) =1 x^{2} +3 x +5(9−8)x2+(−3+)x+(9−4)=1x2+3x+5

STEP 6

Finally, we simplify the expression by removing the coefficient1 in front of x2x^{2}x2.1x2+3x+5=x2+3x+51 x^{2} +3 x +5 = x^{2} +3 x +51x2+3x+5=x2+3x+5The simplified form of the given expression is x2+3x+5x^{2} +3 x +5x2+3x+5.

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QuestionSimplify the expression: $(9 x^{2}+9-3 x)-(4-6 x+8 x^{2})$ .

Assumptions1. We are given the expression $\left(9 x^{}+9-3 x\right)-\left(4-6 x+8 x^{}\right)$ . We need to simplify this expression by combining like terms

Next, we rearrange the terms so that like terms are together.
$9 x^{2}+9-3 x - +6 x -8 x^{2} =9 x^{2} -8 x^{2} -3 x +6 x +9 -$

Now, we combine the like terms.
$9 x^{2} -8 x^{2} -3 x +6 x +9 -4 = (9 -8) x^{2} + (-3 +6) x + (9 -4)$

Perform the operations inside the parentheses.
$(9 -8) x^{2} + (-3 +) x + (9 -4) =1 x^{2} +3 x +5$

Finally, we simplify the expression by removing the coefficient1 in front of $x^{2}$ .
$1 x^{2} +3 x +5 = x^{2} +3 x +5$ The simplified form of the given expression is $x^{2} +3 x +5$ .