Math / Algebra

QuestionWhich expression is equivalent to $\left(3 x^{2}-7\right)$ ? $\left(2 x^{2}-11\right)-\left(x^{2}+4\right)$ $\left(5 x^{2}-6\right)-\left(2 x^{2}-1\right)$ $\left(10 x^{2}-4\right)-\left(7 x^{2}+3\right)$ $\left(15 x^{2}+8\right)-\left(18 x^{2}+1\right)$

Studdy Solution

STEP 1

1. We need to find an expression equivalent to $3x^2 - 7$ .
2. We have four candidate expressions to evaluate.

STEP 2

1. Simplify each candidate expression.
2. Compare each simplified expression to $3x^2 - 7$ .
3. Identify the equivalent expression.

STEP 3

Simplify the first candidate expression: $(2x^2 - 11) - (x^2 + 4)$ .
$= 2x^2 - 11 - x^2 - 4$ $= (2x^2 - x^2) + (-11 - 4)$ $= x^2 - 15$

STEP 4

Simplify the second candidate expression: $(5x^2 - 6) - (2x^2 - 1)$ .
$= 5x^2 - 6 - 2x^2 + 1$ $= (5x^2 - 2x^2) + (-6 + 1)$ $= 3x^2 - 5$

STEP 5

Simplify the third candidate expression: $(10x^2 - 4) - (7x^2 + 3)$ .
$= 10x^2 - 4 - 7x^2 - 3$ $= (10x^2 - 7x^2) + (-4 - 3)$ $= 3x^2 - 7$

STEP 6

Simplify the fourth candidate expression: $(15x^2 + 8) - (18x^2 + 1)$ .
$= 15x^2 + 8 - 18x^2 - 1$ $= (15x^2 - 18x^2) + (8 - 1)$ $= -3x^2 + 7$

STEP 7

Compare each simplified expression to $3x^2 - 7$ .
- First candidate: $x^2 - 15 \neq 3x^2 - 7$ - Second candidate: $3x^2 - 5 \neq 3x^2 - 7$ - Third candidate: $3x^2 - 7 = 3x^2 - 7$ - Fourth candidate: $-3x^2 + 7 \neq 3x^2 - 7$

STEP 8

The expression equivalent to $3x^2 - 7$ is:
$\boxed{(10x^2 - 4) - (7x^2 + 3)}$

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QuestionWhich expression is equivalent to $\left(3 x^{2}-7\right)$ ? $\left(2 x^{2}-11\right)-\left(x^{2}+4\right)$ $\left(5 x^{2}-6\right)-\left(2 x^{2}-1\right)$ $\left(10 x^{2}-4\right)-\left(7 x^{2}+3\right)$ $\left(15 x^{2}+8\right)-\left(18 x^{2}+1\right)$

Studdy Solution

STEP 1

1. We need to find an expression equivalent to $3x^2 - 7$ .
2. We have four candidate expressions to evaluate.

STEP 2

1. Simplify each candidate expression.
2. Compare each simplified expression to $3x^2 - 7$ .
3. Identify the equivalent expression.

STEP 3

Simplify the first candidate expression: $(2x^2 - 11) - (x^2 + 4)$ .
$= 2x^2 - 11 - x^2 - 4$ $= (2x^2 - x^2) + (-11 - 4)$ $= x^2 - 15$

STEP 4

Simplify the second candidate expression: $(5x^2 - 6) - (2x^2 - 1)$ .
$= 5x^2 - 6 - 2x^2 + 1$ $= (5x^2 - 2x^2) + (-6 + 1)$ $= 3x^2 - 5$

STEP 5

Simplify the third candidate expression: $(10x^2 - 4) - (7x^2 + 3)$ .
$= 10x^2 - 4 - 7x^2 - 3$ $= (10x^2 - 7x^2) + (-4 - 3)$ $= 3x^2 - 7$

STEP 6

Simplify the fourth candidate expression: $(15x^2 + 8) - (18x^2 + 1)$ .
$= 15x^2 + 8 - 18x^2 - 1$ $= (15x^2 - 18x^2) + (8 - 1)$ $= -3x^2 + 7$

STEP 7

Compare each simplified expression to $3x^2 - 7$ .
- First candidate: $x^2 - 15 \neq 3x^2 - 7$ - Second candidate: $3x^2 - 5 \neq 3x^2 - 7$ - Third candidate: $3x^2 - 7 = 3x^2 - 7$ - Fourth candidate: $-3x^2 + 7 \neq 3x^2 - 7$

STEP 8

The expression equivalent to $3x^2 - 7$ is:
$\boxed{(10x^2 - 4) - (7x^2 + 3)}$

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Studdy Solution

STEP 1

1. We need to find an expression equivalent to 3x2−7 3x^2 - 7 3x2−7.2. We have four candidate expressions to evaluate.

STEP 2

1. Simplify each candidate expression.2. Compare each simplified expression to 3x2−7 3x^2 - 7 3x2−7.3. Identify the equivalent expression.

STEP 3

Simplify the first candidate expression: (2x2−11)−(x2+4)(2x^2 - 11) - (x^2 + 4)(2x2−11)−(x2+4).=2x2−11−x2−4= 2x^2 - 11 - x^2 - 4=2x2−11−x2−4 =(2x2−x2)+(−11−4)= (2x^2 - x^2) + (-11 - 4)=(2x2−x2)+(−11−4) =x2−15= x^2 - 15=x2−15

STEP 4

Simplify the second candidate expression: (5x2−6)−(2x2−1)(5x^2 - 6) - (2x^2 - 1)(5x2−6)−(2x2−1).=5x2−6−2x2+1= 5x^2 - 6 - 2x^2 + 1=5x2−6−2x2+1 =(5x2−2x2)+(−6+1)= (5x^2 - 2x^2) + (-6 + 1)=(5x2−2x2)+(−6+1) =3x2−5= 3x^2 - 5=3x2−5

STEP 5

Simplify the third candidate expression: (10x2−4)−(7x2+3)(10x^2 - 4) - (7x^2 + 3)(10x2−4)−(7x2+3).=10x2−4−7x2−3= 10x^2 - 4 - 7x^2 - 3=10x2−4−7x2−3 =(10x2−7x2)+(−4−3)= (10x^2 - 7x^2) + (-4 - 3)=(10x2−7x2)+(−4−3) =3x2−7= 3x^2 - 7=3x2−7

STEP 6

Simplify the fourth candidate expression: (15x2+8)−(18x2+1)(15x^2 + 8) - (18x^2 + 1)(15x2+8)−(18x2+1).=15x2+8−18x2−1= 15x^2 + 8 - 18x^2 - 1=15x2+8−18x2−1 =(15x2−18x2)+(8−1)= (15x^2 - 18x^2) + (8 - 1)=(15x2−18x2)+(8−1) =−3x2+7= -3x^2 + 7=−3x2+7

STEP 7

STEP 8

The expression equivalent to 3x2−7 3x^2 - 7 3x2−7 is:(10x2−4)−(7x2+3) \boxed{(10x^2 - 4) - (7x^2 + 3)} (10x2−4)−(7x2+3)​

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1. We need to find an expression equivalent to $3x^2 - 7$ .
2. We have four candidate expressions to evaluate.

1. Simplify each candidate expression.
2. Compare each simplified expression to $3x^2 - 7$ .
3. Identify the equivalent expression.

Simplify the first candidate expression: $(2x^2 - 11) - (x^2 + 4)$ .
$= 2x^2 - 11 - x^2 - 4$ $= (2x^2 - x^2) + (-11 - 4)$ $= x^2 - 15$

Simplify the second candidate expression: $(5x^2 - 6) - (2x^2 - 1)$ .
$= 5x^2 - 6 - 2x^2 + 1$ $= (5x^2 - 2x^2) + (-6 + 1)$ $= 3x^2 - 5$

Simplify the third candidate expression: $(10x^2 - 4) - (7x^2 + 3)$ .
$= 10x^2 - 4 - 7x^2 - 3$ $= (10x^2 - 7x^2) + (-4 - 3)$ $= 3x^2 - 7$

Simplify the fourth candidate expression: $(15x^2 + 8) - (18x^2 + 1)$ .
$= 15x^2 + 8 - 18x^2 - 1$ $= (15x^2 - 18x^2) + (8 - 1)$ $= -3x^2 + 7$

The expression equivalent to $3x^2 - 7$ is:
$\boxed{(10x^2 - 4) - (7x^2 + 3)}$