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 + x
^{2} + 1) and 5x
(ii) (am + bm
^{2} + 5m) and m
^{2}
(iii) (1 + z + z
^{3}) and 9z
(iv) (5p – 3pq + 7q) and (–p
^{5})
(v) (p + q + r) and (-p)
(vi) (y – z + x) and (-4x)
(vii) (mn + m
^{2}n + 5mn
^{2}) and m
^{2}n
^{2}
(viii) (2b
^{2} + 3a
^{2} + 5a
^{3}b) and ab
(ix) (3x
^{2} – 2x
^{2}y + 9y
^{2}) and (–y
^{2})
(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) 6p
^{3}q
^{2}s
^{2} and (2p
^{2}q – 3p
^{3}s
^{2} – 4q
^{3}s)
(v) (-5x
^{2}y
^{3}z
^{4}) and (3x
^{3}y
^{2} – 2x
^{2}yz
^{3} – 7xy
^{2}z
^{2})
(vi) (-5ab
^{2}c) and (4a
^{2}b + 5bc
^{2} – 9cb
^{2})
(vii) (-mn) and (m
^{2} – 2n
^{2} + 3m
^{2}n
^{2})
(viii) (-2pq
^{2}r) and (-4pq – 3qr – 2pr)
(ix) 3ab
^{3}c and (-2a
^{3}b
^{2} – 3a
^{3}c
^{2} – 4b
^{3}c
^{2})
(x) (pqr
^{2}) and (p
^{2}qr + pq
^{2}r – 7pqr
^{2})
3. Find the product
of:
(i) 10ab(ab + bc + ca)
(ii) (-15a
^{2})(1 + ax + by)
(iii) 4m
^{2}n(mn + 1 – n
^{2})
(iv) axy(ax – yx + ay)
(v) -11ab
^{2}c(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) 5x
^{2} + 5x
^{3} + 5x
(ii) am
^{3} + bm
^{4} + 5m
^{3}
(iii) 9z + 9z
^{2} + 9z
^{4}
(iv) -5p
^{6} + 3p
^{6}q – 7p
^{5}q
(v) –p
^{2} –pq - pr
(vi) -4xy + 4xz - 4x
^{2}
(vii) m
^{3}n
^{3} + m
^{4}n
^{3} + 5m
^{3}n
^{4}
(viii) 2ab
^{3} + 3a
^{3}b + 5a
^{4}b
^{2}
(ix) -3x
^{2}y
^{3}+ 2x
^{2}y
^{4} – 9y
^{5}
(x) a
^{2}b
^{2}c – ab
^{2}c
^{2} – a
^{2}bc
^{2}
2. (i) 6pq – 14q
^{2} + 2qr
(ii) -2ac + 4bc – 6c
^{2}
(iii) -8a
^{2}b
^{2}c – 6ab
^{2}c
^{2} – 4a
^{2}bc
^{2}
(iv) 12p
^{5}q
^{3}s
^{2} – 18p
^{6}q
^{2}s
^{4} – 24p
^{3}q
^{5}s
^{3}
(v) -15x
^{5}y
^{5}z
^{4} + 10x
^{4}y
^{4}z
^{7} + 35x
^{3}y
^{5}z
^{6}
(vi) -20a
^{3}b
^{3}c – 25ab
^{3}c
^{3} + 45ab
^{4}c
^{2}
(vii) –m
^{3}n + 2mn
^{3} – 3m
^{3}n
^{3}
(viii) 8p
^{2}q
^{3}r + 6pq
^{3}r
^{2} + 4p
^{2}q
^{2}r
^{2}
(ix) -6a
^{4}b
^{5}c – 9a
^{4}b
^{3}c
^{3} – 12ab
^{6}c
^{3}
(x) p
^{3}q
^{2}r
^{3} + p
^{2}q
^{3}r
^{3} - 7p
^{2}q
^{2}r
^{4}
3. (i) 10a
^{2}b
^{2} + 10ab
^{2}c + 10a
^{2}bc
(ii) -15a
^{2} – 15a
^{3}x -15a
^{2}by
(iii) 4m
^{3}n
^{2} + 4m
^{2}n – 4m
^{2}n
^{3}
(iv) a
^{2}x
^{2}y – ax
^{2}y
^{2} + a
^{2}xy
^{2}
(v) -11a
^{2}b
^{3}c – 22ab
^{3}c
^{2} + 44a
^{2}b
^{2}c
^{2}
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