1. Multiplying monomial with polynomial

2. Monomial
An algebraic expression which contains only one term
is known as Monomial 
Example : 2x, 3x2, 4t, 9p2q, -8mn2
Multiply Monomials by Polynomials
Monomial is outside the parenthesis (bracket).
Polynomial is inside the parenthesis.
Use a distributive property to open the parenthesis.
Distributive property --->Multiply each term of the parenthesis by the
monomial keeping the addition or subtraction sign same.

3. Example 1: Multiply (5a) and (3a6 + 2a + 5) Solution:
Monomial
3a6 + 2a + 5
polynomial
Write in the multiplication expression and we get: 5a x (3a6 + 2a + 5)
Use Distributive Law and multiply monomial with every term of polynomial
& this is done in the following steps: x
5a x (3a6 + 2a + 5) = 5a x 3a a x 2a a x 5
= (5 x 3) (a x a6) + (5 x 2) (a x a) + (5 x 5) a
= 15a a a x x
Multiply the co-efficients and
variables separately.
For variables, add the exponents,
a x a = a1+1 = a (a = a1)
a x a6 = a1+6 = a (a = a1)
Ans: 5a x (3a6 + 2a + 5) = 15a7 + 10a2 + 25a

4. Example 2: Multiply (-3a) and (3a2 - 7a + 4) Solution:
polynomial
-3a
3a2 - 7a + 4
Monomial
Write in the multiplication expression and we get: (-3a) x (3a2 - 7a + 4)
Use Distributive Law and multiply monomial with every term of
polynomial & this is done in the following steps: x
= (-3a) x 3a (-3a) x (7a) (-3a) x 4
= (-3 x 3) (a x a2) - (-3 x 7) (a x a) + (-3 x 4) a
= -9a (-21)a (-12)a
= -9a a a
(-3a) x (3a2 - 7a + 4) x x
Multiply the co-efficients and
variables separately.
For variables, add the exponents,
a x a = a1+1 = a (a = a1)
a x a2 = a1+2 = a (a = a1)
Multiplication rule of integers
- x - = + , + x + = +
- x + = - , + x - = -
Ans: (-3a) x (3a2 – 7a+4) = -9a3 + 21a2 - 12a

5. Try These
Multiply (5h4) x (h5+7h+8)
Multiply (-4n) x (n2+3n-10)