write the name of the tools used in photoshop write vertical text
Answers
Explanation:
Case 2 :
From case 1,
a3 - b3 = (a - b)3 + 3ab(a - b)
a3 - b3 = (a - b)[(a - b)2 + 3ab]
a3 - b3 = (a - b)[a2 - 2ab + b2 + 3ab]
a3 - b3 = (a - b)(a2 + ab + b2)
Therefore, the formula for (a3 - b3) is
a3 - b3 = (a - b)(a2 + ab + b2)
So,
(a - b) and (a2 + ab + b2)
are the factors of (a3 - b3).
Note :
Based on our need, either we can use the formula in case 1 or in case 2 for (a3 - b3).
Practice Questions
Question 1 :
Factor :
x3 - 1
Solution :
Write (x3 - 1) in the form of (a3 - b3).
x3 - 1 = x3 - 13
(x3 - 13) is in the form of (a3 - b3).
Comparing (a3 - b3) and (x3 - 13), we get
a = x
b = 1
Write the formula for (a3 - b3) given in case 2 above.
a3 - b3 = (a - b)(a2 + ab + b2)
Substitute x for a and 1 for b.
x3 - 13 = (x - 2)(x2 + x(1) + 12)
x3 + 1 = (x - 1)(x2 + x + 1)
Question 2 :
Factor :
8x3 - 27y3
Solution :
Write (8x3 - 27y3) in the form of (a3 - b3).
8x3 - 27y3 = (2x)3 - (3y)3
(2x)3 - (3y)3 is in the form of (a3 - b3).
Comparing (a3 - b3) and (2x)3 - (3y)3, we get
a = 2x
b = 3y
Write the formula for (a3 - b3) given in case 2 above.
a3 - b3 = (a - b)(a2 + ab + b2)
Substitute 2x for a and 3y for b.
(2x)3 - (3y)3 = (2x - 3y)[(2x)2 + (2x)(3y) + (3y)2]
8x3 - 27y3 = (2x - 3y)(4x2 + 6xy + 9y2)
Question 3 :
Factor :
125p3 - 64q3
Solution :
Write (125p3 - 64q3) in the form of (a3 - b3).
125p3 - 64q3 = (5p)3 - (4q)3
(5p)3 - (4q)3 is in the form of (a3 - b3).
Comparing (a3 - b3) and (5p)3 - (4q)3, we get
a = 5p
b = 4q
Write the formula for (a3 - b3) given in case 2 above.
a3 - b3 = (a - b)(a2 + ab + b2)
Substitute 5p for a and 4q for b.
(5p)3 - (4q)3 = (5p - 4q)[(5p)2 + (5p)(4q) + (4q)2]
125p3 - 64q3 = (5p - 4q)(25p2 + 20pq + 16q2)
Question 4 :
Find the value of (m3 - n3), if m - n = 3 and mn = 28.
Solution :
Write (m3 - n3) in terms of (m - n) and mn using the formula given in case 1 above.
m3 - n3 = (m - n)3 + 3mn(m - n)
Substitute 3 for (m - n) and 28 for xy.
x3 - y3 = (3)3 + 3(28)(3)
x3 - y3 = 27 + 252
x3 - y3 = 2