 Worksheet on Multiplying Monomial and Polynomial will assist students in learning the multiplication of algebraic expressions involving Monomial and Polynomial. Learn the necessary math skill so that you will find it easy while solving complex algebraic expressions. Multiplication of Monomial and Polynomial Worksheet will offer step by step explanation for all the problems within so that you will get to know the algebraic methods used in solving the polynomial and monomial multiplication expressions.

Multiplying Monomial and Polynomial Worksheet with Answers will guide you in having an in-depth understanding of the concept as well get grip on the rules associated with it. Attain and Fluency by answering the questions from the Free Printable Math Multiplication of Monomial and Polynomial Worksheet on a frequent basis.

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## Multiplication of a Monomial and Polynomial Worksheet

I. Multiply monomial by polynomial:
(i) 4x and (2x – 3y + 5z)
(ii) (-5m) and (3m – 4n + 2p)
(iii) 6xyz and (-7xy – 2yz – zx)
(iv) 7a3b2c2 and (4a2b – 2a3c2 – b3c)
(v) (-2x3y2z4) and (4x4y3 – 3x3y2z3 – 6xy2z2y)

Solution:

(i) Given 4x and (2x – 3y + 5z)
Multiply the monomial with every term of the polynomial
=4x(2x)-3y(4x)+5z(4x)
=8x2-12xy+20xz
Hence, By multiplying 4x and (2x – 3y + 5z) is 8x2-12xy+20xz.
(ii) Given (-5m) and (3m – 4n + 2p)
Multiply the monomial with every term of the polynomial
=(-5m)(3m) -4n(-5m)+ 2p(-5m)
=-15m2+20mn-10pm
Hence, By multiplying (-5m) and (3m – 4n + 2p) we get -15m2+20mn-10pm.
(iii) Given 6xyz and (-7xy – 2yz – zx)
Multiply the monomial with every term of the polynomial
=6xyz(-7xy)-2yz(6xyz)-zx(6xyz)
=-42x2y2z-12xy2z2-6x2yz2
Hence, By multiplying 6xyz and (-7xy – 2yz -zx) we get -42x2y2z-12xy2z2-6x2yz2.
(iv) Given 7a3b2c2 and (4a2b – 2a3c2 – b3c)
Multiply the monomial with every term of the polynomial
=4a2b(7a3b2c2)-2a3c2(7a3b2c2 )-b3c(7a3b2c2)
=28a5b3c2-14a6b2c4-7a3b5c3
Hence, By multiplying 7a3b2c2 and (4a2b – 2a3c2 – b3c)  we get 28a5b3c2-14a6b2c4-7a3b5c3  .
(v) Given (-2x3y2z4) and (4x4y3 – 3x3y2z3 – 6xy2z2)
Multiply the monomial with every term of the polynomial
=4x4y3((-2x3y2z4) -3x3y2z3(-2x3y2z4) -6xy2z2(-2x3y2z4)
=-8x7y5z4+6x6y4z7+12x4y4z6
Hence, By multiplying (-2x3y2z4)  and (4x4y3 – 3x3y2z3 – 6xy2z2)  we get -8x7y5z4+6x6y4z7+12x4y4z6.

II. Multiply polynomial by monomial:
(i) (m+ m4 + 1) and 5m
(ii) (ax2 + bx3 + 5x) and x2
(iii) (2x + xz + z3) and 7z
(iv) (m – 2mn + 8n) and (–m7)
(v) (a + 2bc + ca) and (-a)

Solution:

(i) Given, (m+ m4 + 1) and 5m
Multiply the monomial with every term of the polynomial
=m(5m) + m4 (5m) + 1(5m)
=5m2+5m5+5m
Therefore, By multiplying (m+ m4 + 1) and 5m we get 5m2+5m5+5m.
(ii) Given, (ax2 + bx3 + 5x) and x2
Multiply the monomial with every term of the polynomial
=ax2(x2) + bx3(x2) + 5x(x2)
=ax4+bx5+5x3
Therefore, By multiplying (ax2 + bx3 + 5x) and x2 we get ax4+bx5+5x3.
(iii) Given, (2x + xz + z3) and 7z
Multiply the monomial with every term of the polynomial
=2x(7z) + xz(7z) + z3 (7z)
=14xz + 7xz2 + 7z4
Therefore, By multiplying (2x + xz + z3) and 7z is 14xz + 7xz2 + 7z4.
(iv) Given, (m – 2mn + 8n) and (–m7)
Multiply the monomial with every term of the polynomial
=m(–m7) – 2mn(–m7) + 8n(–m7)
=-m8+2m8n-8m7n
Therefore, By multiplying (m – 2mn + 8n) and (–m7) we get -m8+2m8n-8m7n.
(v) Given,(a + 2bc + ca) and (-a)
Multiply the monomial with every term of the polynomial
=a(-a)+2bc(-a)+ca(-a)
=-a2-2abc-a2c
Therefore, By multiplying (a + 2bc + ca) and (-a) we get -a2-2abc-a2c.

III. Find the product of the following:
(i) 3ab(2ab + b2c + 5ca)
(ii) (-13m2)(5 + mx + ny)
(iii) 2m2n(mn + n – n2)
(iv) mn(m2+n2)
(v) -6a2bc(3ab + bc – 7ca)
(vi) (x+3y)(2x+6y)

Solution:

(i) Given, 3ab(2ab + b2c + 5ca)
Multiply the monomial with every term of the polynomial
=3ab(2ab)+b2c(3ab) + 3ab(5ca)
=6a2b2 + 3ab3c + 15a2bc
Hence, By multiplying 3ab(2ab + b2c + 5ca) we get 6a2b2 + 3ab3c + 15a2bc.
(ii) Given, (-13m2)(5 + mx + ny)
Multiply the monomial with every term of the polynomial
=(-13m2)5 + mx((-13m2) + ny(-13m2)
=-65m2-13m3x-13m2ny
Hence, By multiplying (-13m2)(5 + mx + ny) we get -65m2-13m3x-13m2ny.
(iii) Given, 2m2n(mn + n – n2)
Multiply the monomial with every term of the polynomial
=2m2n(mn) + n(2m2n)-n2(2m2n)
=2m3n2+2m2n2-2m2n3
Hence, By multiplying 2m2n(mn + n – n2) we get 2m3n2+2m2n2-2m2n3.
(iv) Given, mn(3m2+2n2)
Multiply the monomial with every term of the polynomial
=mn(3m2) + mn(2n2)
=3m3n + 2mn3
Hence, By multiplying mn(m2+n2) we get 3m3n + 2mn3.
(v) Given, -6a2bc(3ab + bc – 7ca)
Multiply the monomial with every term of the polynomial
=-6a2bc(3ab) + bc(-6a2bc) -7ca(-6a2bc)
=-18a3b2c-6a2b2c2+42a3bc2
Hence, By multiplying -6a2bc(3ab + bc – 7ca) we get -18a3b2c-6a2b2c2+42a3bc2.
(vi) Given, (x+3y)(2x+6y)
By using the distributive property, multiply the polynomials,
=x(2x+6y) + 3y(2x+6y)
=2×2+6xy+6yx+18y2
=2×2+12xy+18y2
Hence, By multiplying (x+3y)(2x+6y) we get 2×2+12xy+18y2.

IV. The product of two numbers is 3m4 if one of them is 1/4m2. Find the other?

Solution:

Given,
The product of two numbers is =3m4
one of the number=1/4m2
Let the other number be x.
1/4m2 × x=3m4
x=3m4.4m2
x=12m6
Therefore, the other number is 12m6.

V. If P=5x2+2x, Q=2x, R=24. Find the value of (P × R)/Q.

Solution:

Given P=5x2+2x, Q=2x+2, R=24
P × R=24(5x2+2x)
=120x2 + 48x
(P × R)/Q= (120x2 + 48x)/2x
=60x+24
Hence, the value of (P × R)/Q is 60x+24.

VI. If the length and width of the rectangle are (-4a2+7) and (2a + 5) respectively. Find the area of the rectangle?

Solution:

Given,
The length of the rectangle=(-4a2+7)
The breadth of the rectangle=(2a + 5)
Area of the rectangle=length * breadth
=(-4a2+7) * (2a + 5)
=-4a2(2a+5) + 7(2a+5)
=-8a3-20a2+14a+35