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)
if we distribute 2(2x+5), we'll end up with 4x + 10, so in short, the right-hand-side, is really the left-hand-side in disguise.
and since 4x + 10 = 4x + 10, both equations are equal, meaning in short, the system has an infinite number of solutions.
The two numbers are 3 and 20.
3 * 20 = 60
3 + 20 = 23
Answer:
Step-by-step explanation:
ΔADC and ΔCBD are similar. Therefore the corresponding sides are in proportion:
We have
AD = 2, CD = X, DB = 6.
Substitute:
<em>cross multiply</em>
