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.

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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