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
^{2}y + 27xy
^{2} + 27y
^{3}
(ii) p
^{3}x
^{3} + 3p
^{2}qx
^{2}y + 3pxq
^{2}y
^{2} + q
^{3}y
^{3}
(iii) x
^{6} + 27x
^{4}y + 243x
^{2}y
^{2} + 729y
^{3}
(iv) -x
^{3} + 6x
^{2}y – 12xy
^{2} + 8y
^{3}
(v) a
^{3} + 24a
^{2}y + 192ay
^{2} + 512y
^{3}
(vi) 1/64 p
^{3} + 9/64 p
^{2}q + 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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