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