Given the expression: 3x^10 − 48x^2

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)

Part A: 3x²(x⁸ - 16)

Part B: 3x²(x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)  

Step-by-step explanation:

Part A. Factor out the greatest common factor

3x¹⁰ - 48 x²

= 3x²(x⁸ - 16)

Part B. Factor the expression completely

(i) Factor the difference of squares

x⁸ - 16

= (x⁴ - 4)(x⁴ + 4)

= (x² - 2)(x² + 2)(x⁴ + 4)

3x¹⁰ - 48 x² = 3x²(x² - 2)(x² + 2)(x⁴ + 4)

(ii) Factor the sum of squares

Use the Sophie Germain Identity to factor x⁴ + 4.

x⁴ + 4

= (x²)² + 2²           (Still a sum of squares)

= (x² + 2)² - 4x²    (Factor this as a difference of squares)

= (x² + 2 - 2x)(x² + 2 + 2x)

3x¹⁰ - 48 x² = 3x² (x² - 2)(x² + 2) (x² - 2x + 2)(x² + 2x + 2)

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.