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Answer:
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)
Answer:
x = 82°
y = 8°
Step-by-step explanation:
x + 98° = 180°
x = 180° - 98°
<u>x = 82°</u>
x + y = 90°
82° + y = 90°
y = 90° - 82°
<u>y = 8°</u>
Answer:
40
Step-by-step explanation:
Try to get the variable alone by dividing 5/8 on both sides of the equations.
That cancels out the 5/8 on the left leaving u and the 25 on the right turns into 40. It turns into 40 because 25 divided by 5/8 equals 40.