Worksheet on Multiplying Monomial and Polynomial

Practice the questions given in the worksheet on multiplying monomial and polynomial. The questions are based on multiplication of a polynomial by a monomial and multiplication of a monomial by a polynomial.

1. Multiply polynomial by monomial:

(i) (x + x² + 1) and 5x

(ii) (am + bm² + 5m) and m²

(iii) (1 + z + z³) and 9z

(iv) (5p – 3pq + 7q) and (–p⁵)

(v) (p + q + r) and (-p)

(vi) (y – z + x) and (-4x)

(vii) (mn + m²n + 5mn²) and m²n²

(viii) (2b² + 3a² + 5a³b) and ab

(ix) (3x² – 2x²y + 9y²) and (–y²)

(x) (-ab + bc + ac) and (-abc)

2. Multiply monomial by polynomial:

(i) 2q and (3p – 7q + r)

(ii) (-2c) and (a – 2b + 3c)

(iii) 2abc and (-4ab – 3bc – 2ac)

(iv) 6p³q²s² and (2p²q – 3p³s² – 4q³s)

(v) (-5x²y³z⁴) and (3x³y² – 2x²yz³ – 7xy²z²)

(vi) (-5ab²c) and (4a²b + 5bc² – 9cb²)

(vii) (-mn) and (m² – 2n² + 3m²n²)

(viii) (-2pq²r) and (-4pq – 3qr – 2pr)

(ix) 3ab³c and (-2a³b² – 3a³c² – 4b³c²)

(x) (pqr²) and (p²qr + pq²r – 7pqr²)

3. Find the product of:

(i) 10ab(ab + bc + ca)

(ii) (-15a²)(1 + ax + by)

(iii) 4m²n(mn + 1 – n²)

(iv) axy(ax – yx + ay)

(v) -11ab²c(5ab + 2bc – 4ca)

Answers for the worksheet on multiplying monomial and polynomial are given below to check the exact answers of the above multiplication.

Answers:

1. (i) 5x² + 5x³ + 5x

(ii) am³ + bm⁴ + 5m³

(iii) 9z + 9z² + 9z⁴

(iv) -5p⁶ + 3p⁶q – 7p⁵q

(v) –p² –pq - pr

(vi) -4xy + 4xz - 4x²

(vii) m³n³ + m⁴n³ + 5m³n⁴

(viii) 2ab³ + 3a³b + 5a⁴b²

(ix) -3x²y³+ 2x²y⁴ – 9y⁵

(x) a²b²c – ab²c² – a²bc²

2. (i) 6pq – 14q² + 2qr

(ii) -2ac + 4bc – 6c²

(iii) -8a²b²c – 6ab²c² – 4a²bc²

(iv) 12p⁵q³s² – 18p⁶q²s⁴ – 24p³q⁵s³

(v) -15x⁵y⁵z⁴ + 10x⁴y⁴z⁷ + 35x³y⁵z⁶

(vi) -20a³b³c – 25ab³c³ + 45ab⁴c²

(vii) –m³n + 2mn³ – 3m³n³

(viii) 8p²q³r + 6pq³r² + 4p²q²r²

(ix) -6a⁴b⁵c – 9a⁴b³c³ – 12ab⁶c³

(x) p³q²r³ + p²q³r³ - 7p²q²r⁴

3. (i) 10a²b² + 10ab²c + 10a²bc

(ii) -15a² – 15a³x -15a²by

(iii) 4m³n² + 4m²n – 4m²n³

(iv) a²x²y – ax²y² + a²xy²

(v) -11a²b³c – 22ab³c² + 44a²b²c²

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