Math / Algebra

Question7. What is the difference $\left(4 x^{2}-12 x+6\right)-\left(10+3 x-2 x^{2}\right)$ ?

Studdy Solution

STEP 1

1. We are given a polynomial expression and asked to find the difference between two polynomials.
2. The expression involves subtraction of two polynomials.
3. Simplifying the expression involves distributing the negative sign and combining like terms.

STEP 2

1. Distribute the negative sign across the second polynomial.
2. Combine like terms.

STEP 3

Distribute the negative sign across the second polynomial $\left(10 + 3x - 2x^2\right)$ :
$\left(4x^2 - 12x + 6\right) - \left(10 + 3x - 2x^2\right) = 4x^2 - 12x + 6 - 10 - 3x + 2x^2$

STEP 4

Combine like terms. Group the terms with $x^2$ , the terms with $x$ , and the constant terms:
$(4x^2 + 2x^2) + (-12x - 3x) + (6 - 10)$

STEP 5

Calculate each group:
$4x^2 + 2x^2 = 6x^2$
$-12x - 3x = -15x$
$6 - 10 = -4$

STEP 6

Combine the results from each group to form the simplified polynomial:
$6x^2 - 15x - 4$
The difference of the given polynomials is:
$\boxed{6x^2 - 15x - 4}$

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Question7. What is the difference $\left(4 x^{2}-12 x+6\right)-\left(10+3 x-2 x^{2}\right)$ ?

Studdy Solution

STEP 1

1. We are given a polynomial expression and asked to find the difference between two polynomials.
2. The expression involves subtraction of two polynomials.
3. Simplifying the expression involves distributing the negative sign and combining like terms.

STEP 2

1. Distribute the negative sign across the second polynomial.
2. Combine like terms.

STEP 3

Distribute the negative sign across the second polynomial $\left(10 + 3x - 2x^2\right)$ :
$\left(4x^2 - 12x + 6\right) - \left(10 + 3x - 2x^2\right) = 4x^2 - 12x + 6 - 10 - 3x + 2x^2$

STEP 4

Combine like terms. Group the terms with $x^2$ , the terms with $x$ , and the constant terms:
$(4x^2 + 2x^2) + (-12x - 3x) + (6 - 10)$

STEP 5

Calculate each group:
$4x^2 + 2x^2 = 6x^2$
$-12x - 3x = -15x$
$6 - 10 = -4$

STEP 6

Combine the results from each group to form the simplified polynomial:
$6x^2 - 15x - 4$
The difference of the given polynomials is:
$\boxed{6x^2 - 15x - 4}$

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Question7. What is the difference (4x2−12x+6)−(10+3x−2x2)\left(4 x^{2}-12 x+6\right)-\left(10+3 x-2 x^{2}\right)(4x2−12x+6)−(10+3x−2x2) ?

Studdy Solution

STEP 1

1. We are given a polynomial expression and asked to find the difference between two polynomials.2. The expression involves subtraction of two polynomials.3. Simplifying the expression involves distributing the negative sign and combining like terms.

STEP 2

1. Distribute the negative sign across the second polynomial.2. Combine like terms.

STEP 3

STEP 4

Combine like terms. Group the terms with x2x^2x2, the terms with xxx, and the constant terms:(4x2+2x2)+(−12x−3x)+(6−10) (4x^2 + 2x^2) + (-12x - 3x) + (6 - 10) (4x2+2x2)+(−12x−3x)+(6−10)

STEP 5

Calculate each group:4x2+2x2=6x2 4x^2 + 2x^2 = 6x^2 4x2+2x2=6x2−12x−3x=−15x -12x - 3x = -15x −12x−3x=−15x6−10=−4 6 - 10 = -4 6−10=−4

STEP 6

Combine the results from each group to form the simplified polynomial:6x2−15x−4 6x^2 - 15x - 4 6x2−15x−4 The difference of the given polynomials is:6x2−15x−4 \boxed{6x^2 - 15x - 4} 6x2−15x−4​

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Question7. What is the difference $\left(4 x^{2}-12 x+6\right)-\left(10+3 x-2 x^{2}\right)$ ?

1. We are given a polynomial expression and asked to find the difference between two polynomials.
2. The expression involves subtraction of two polynomials.
3. Simplifying the expression involves distributing the negative sign and combining like terms.

1. Distribute the negative sign across the second polynomial.
2. Combine like terms.

Combine like terms. Group the terms with $x^2$ , the terms with $x$ , and the constant terms:
$(4x^2 + 2x^2) + (-12x - 3x) + (6 - 10)$

Calculate each group:
$4x^2 + 2x^2 = 6x^2$
$-12x - 3x = -15x$
$6 - 10 = -4$

Combine the results from each group to form the simplified polynomial:
$6x^2 - 15x - 4$
The difference of the given polynomials is:
$\boxed{6x^2 - 15x - 4}$