PLEASE HELP
Given the expression: 3x10 - 48x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

a.  3x^2 ( x^8 - 16 )

b.  3x^2 ( x^2     - 2 )  (x^2 +2)( x^4   +4 )

Step-by-step explanation:

3x^10 - 48x^2

We can factor out 3 x^2

3x^2 ( x^8 - 16 )

We know the terms inside the parentheses is the difference of squares and

(a^2 -b^2) = (a-b) (a+b)

3x^2 ( x^4 ^2   - 4^2 )

3x^2 ( x^4    - 4 )( x^4   +4 )

The first term in parentheses is the difference of squares

3x^2 ( x^2 ^2    - 2^2 )( x^4   +4 )

3x^2 ( x^2     - 2 )  (x^2 +2)( x^4   +4 )

A) 3x²(x⁸ - 16)

B) 3x²(x⁴ + 4)(x² - 2)(x² + 2)

Step-by-step explanation:

3x¹⁰ - 48x²

3x²(x⁸ - 16)

3x²[(x⁴)² - 4²]

3x²[(x⁴ - 4)(x⁴ + 4)]

3x²(x⁴ + 4)[(x²)² - 2²]

3x²(x⁴ + 4)(x² - 2)(x² + 2)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1