Question
Factorize the following expressions:
27x3 - y3 - z3 - 9xyz
27x3 - y3 - z3 - 9xyz
✓
Answer
We know that
x3 + y3 + z3 - 3xyz = ( x + y + z)(x2 + y2 + z2 - xy - yz -zx)
$\therefore$ 27x3 - y3 - z3 - 9xyz
= (3x)3 + (-y)3 + (-z)3 - 3(3x)(-y)(-z)
= [3x +(-y) + (-z)][(3x)2 + (-y)2 + (-z)2 - (3x)(-y)(-z)-(-z)(3x)]
= (3x - y - z)(9x2 + y2 + z2 + 3xy - yz + 3zx)
x3 + y3 + z3 - 3xyz = ( x + y + z)(x2 + y2 + z2 - xy - yz -zx)
$\therefore$ 27x3 - y3 - z3 - 9xyz
= (3x)3 + (-y)3 + (-z)3 - 3(3x)(-y)(-z)
= [3x +(-y) + (-z)][(3x)2 + (-y)2 + (-z)2 - (3x)(-y)(-z)-(-z)(3x)]
= (3x - y - z)(9x2 + y2 + z2 + 3xy - yz + 3zx)
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Read the Source/ Text given below and answer these questions:
Arun is participating in an 8 miles walk. The organizers used a square coordinate grid to plot the course. The starting point is at A (3, 1). At B (3, 4), there's a water station to make sure the walkers stay hydrated. From water station, the walkway turns right and at C (6,4) a garden is situated to keep walkers fresh. From the garden, the walkway turns left and finally, Arun reaches at destination D to complete 8 miles.
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1. What is the abscissa of destination point D?
2. What is the ordinate of destination point D?
Arun is participating in an 8 miles walk. The organizers used a square coordinate grid to plot the course. The starting point is at A (3, 1). At B (3, 4), there's a water station to make sure the walkers stay hydrated. From water station, the walkway turns right and at C (6,4) a garden is situated to keep walkers fresh. From the garden, the walkway turns left and finally, Arun reaches at destination D to complete 8 miles.
questions:
1. What is the abscissa of destination point D?
2. What is the ordinate of destination point D?