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)

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x