Worksheet on Cube of the Sum of Two Binomials
Practice the questions given in the
worksheet on cube of the sum of two binomials. We know, cube of a binomial
means multiplying a binomial with itself three times.
See the formulas to expand the cube of the sum
of two binomials.
1.
Expand each of the following:
(i) (x + 3y)
3
(ii) (px + qy)
3
(iii) (x
2 + 9y)
3
(iv) (-x + 2y)
3
(v) (a + 8y)
3
(vi) (1/4 p + 3/4 q)
3
2. Evaluate by using suitable identity.
(i) (105)
3
(ii) (1002)
3
(iii) (303)
3
(iv) (10.1)
3
(v) (9.04)
3
3. (i) If x + 1/x = 7, find the value of x
3 + 1/x
3
(ii) If x + 1/x = 11, find the value of x
3 + 1/x
3
4. (i) Find the value of 125x
3 + 27y
3, if 5x + 3y = 8 and xy = 2.
(ii) Find the value of 8x
3 + 64y
3, if 2x + 4y = 12 and xy = 5.
Answers for the worksheet on cube of the
sum of two binomials are given below to check the exact answers of the above
expansion.
Answers:
1. (i) x
3 + 9x
2y + 27xy
2 + 27y
3
(ii) p
3x
3 + 3p
2qx
2y + 3pxq
2y
2 + q
3y
3
(iii) x
6 + 27x
4y + 243x
2y
2 + 729y
3
(iv) -x
3 + 6x
2y – 12xy
2 + 8y
3
(v) a
3 + 24a
2y + 192ay
2 + 512y
3
(vi) 1/64 p
3 + 9/64 p
2q + 27/64 pq
2 + 27/64 q
3
2. (i) 1157625
(ii) 1006012008
(iii) 27818127
(iv) 1030.301
(v) 738.763264
3. (i) 322 (ii) 1298
4. (i) -208 (ii) 288
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