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) (x2 + 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 x3 + 1/x3

(ii) If x + 1/x = 11, find the value of x3 + 1/x3


4. (i) Find the value of 125x3 + 27y3, if 5x + 3y = 8 and xy = 2.

(ii) Find the value of 8x3 + 64y3, 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) x3 + 9x2y + 27xy2 + 27y3

(ii) p3x3 + 3p2qx2y + 3pxq2y2 + q3y3

(iii) x6 + 27x4y + 243x2y2 + 729y3

(iv) -x3 + 6x2y – 12xy2 + 8y3

(v) a3 + 24a2y + 192ay2 + 512y3

(vi) 1/64 p3 + 9/64 p2q + 27/64 pq2 + 27/64 q3


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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