Worksheet on the Product of two Binomials whose First Terms are Same and Second Terms are Different

Practice the questions given in the worksheet on the product of two binomials whose first terms are same and second terms are different.

See the identities to find the products of two binomials using the formulas.

1. Use the formula (x + a) (x + b) = x² + x(a + b) + ab to identity to find the following products.

(i) (x + 5) (x + 6)

(ii) (x + 7) (x + 10)

(iii) (x + 9) (x + 8)

(iv) (x + 3) (x + 8)

2. Use the formula (x + a) (x - b) = x² + x (a – b) – ab to identity to find the following products.

(i) (x + 3) (x – 7)

(ii) (x + 5) (x – 2)

(iii) (t + 7) (t – 5)

(iv) (t + 9) (t – 4)

3. Use the formula (x - a) (x - b) = x² – x (a + b) + ab to identity to find the following products.

(i) (a – 3) (a – 2)

(ii) (a – 5) (a – 11)

(iii) (a – 1) (a – 1)

4. Use the formula (x - a) (x + b) = x² + x (b – a) – ab to identity to find the following products.

(i) (m – 5) (m + 19)

(ii) (m – 6) (m + 13)

(iii) (m - 2) (m + 6)

(iv) (m – 4) (m + 1)

5. Evaluate the following products using the specific formula.

(i) (x + 1/4) (x + 4)

(ii) (x + 7) (x + 4/9)

(iii) (y - 3/4) (y - 4/3)

(iv) (y² – 4) (y² – 9)

(v) (z² + 9) (z² – 1/3)

(vi) (z² + √4) (z² - √9)

(vii) (p³ – 8/3) (p³ + 4/9)

(viii) (3a² – 4b²) (3a² + 5b²)

6. Evaluate the following products without direct multiplication.

(i) 102 × 105

(ii) 203 × 204

(iii) 96 × 97

(iv) 80 × 81

(v) 97 × 103

(vi) 197 × 205

(vii) 304 × 293

(viii) 193 × 189

(ix) 86 × 83

(x) 96 × 101

(xi) 204 × 197

(xii) 195 × 189

(xiii) 104 × 106

(xiv) 52 × 61

Answers for the worksheet on the product of two binomials whose first terms are same and second terms are different are given below to check the exact answers of the above evaluation.

Answers:

1. (i) x² + 11x 30

(ii) x² + 17x + 70

(iii) x² + 17x + 72

(iv) x² + 11x + 24

2. (i) x² – 4x – 21

(ii) x² + 3x – 10

(iii) t² + 2t – 35

(iv) t² + 5t – 36

3. (i) a² – 5a + 6

(ii) a² – 16a + 55

(iii) a² – 5a + 4

4. (i) m² + 14m – 95

(ii) m² + 7m – 78

(iii) m² + 4m – 12

(iv) m² – 3m – 4

5. (i) x² + 17/4 x + 1

(ii) x² + 67/9 x + 28/9

(iii) y² – 25/12 y + 1

(iv) y⁴ – 13y² + 36

(v) z⁴ + 26/3 z² – 3

(vi) z⁴ – z² – 6

(vii) p⁴ – 20/9 p² – 32/27

(viii) 9a⁴ + 3a²b² – 20b⁴

6. (i) 10710

(ii) 41412

(iii) 9312

(v) 7209

(v) 9991

(vi) 40385

(vii) 89072

(viii) 36477

(ix) 7138

(x) 9696

(xi) 40188

(xii) 36855