1. Multiplying monomial with binomial

2. Monomial
An algebraic expression which contains only one term
is known as Monomial 
Example : 2x, 3x2, 4t, 9p2q, -8mn2
Multiply Monomials by Binomials
Monomial is outside the parenthesis (bracket).
Binomial is inside the parenthesis.
Use 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 2a and (3a - 4) Solution:
Monomial
3a - 4
Binomial
Write in the multiplication expression and we get: 2a x (3a - 4)
Use Distributive Law and multiply monomial with every term of binomial &
this is done in the following steps: x
= 2a x 3a – 2a x 4
= (2 x 3) (a x a) – (2 x 4) a
= 6a – a
2a x (3a - 4) x
Multiply the numerical coefficients and
variables separately.
For variables, add the power of exponents,
a x a = a1+1 = a (a = a1)
Ans: 2a x (3a – 4) = 6a2 – 8a

4. Example 2: Multiply (-3f) and (5f + f6) Solution:
Monomial
Binomial
Write in the multiplication expression and we get: (-3f) x (5f + f6)
Use Distributive Law and multiply monomial with every term of
binomial & this is done in the following steps: x
(-3f) x (5f + f6)
= (-3f) x 5f + (-3f) x f6
= (-3 x 5) (f x f) + (-3) (f x f6)
= -15f2 – 3f7
Multiply the numerical coefficients and
variables separately. x
For variables, add the exponents,
f x f = f1+1 = f2 (f = f1)
f x f6 = f1+6 = f7 (f = f1)
Ans: (-3f) x (5f + f6) = -15f2 – 3f7

5. Example 3: Multiply 3ab and (a2b – ab2) Solution:
Monomial
a2b – ab2
Binomial
Write in the multiplication expression and we get: 3ab x (a2b – ab2)
Use Distributive Law and multiply monomial with every term of
binomial & this is done in the following steps: x
Multiply variables with the base of
a and b separately.
= 3ab x a2b – 3ab x ab2
= 3 (a x a2) (b x b) – 3 (a x a) (b x b2)
= 3a3b – 3a2b3
3ab x (a2b – ab2) x
For variables, add the powers exponents,
a x a2 = a1+2 = a (a = a1)
b x b = b1+1 = b (b = b1)
a x a = a1+1 = a (a = a1)
b x b2 = b1+2 = b (b = b1)
Ans: 3ab x (a2b – ab2) = 3a3b2 – 3a2b3

6. Try These
Multiply (6b4) and (b+7)
Multiply (-5h2) and (h5+7h)