1. Multiplying binomial with polynomial

2. Binomial An algebraic expression which contains two terms
is known as Binomial 
Example 1 : 2x + 3x2 
It is a Binomial, because it contains two terms 2x and 3x2 
Example 2 : 9pq + 11p2q
It is a Binomial, because it contains two terms 9pq and 11p2q

3. Multiply binomial with polynomial
Step1:- Multiply each term of Binomial with polynomial keeping
the addition or subtraction sign same.
Step2:- Combine all the like terms

4. Example 1: Multiply (x + 3) and (x2 + y + 5) Solution:
Polynomial
(x + 3)
Binomial
Write in the expression form product of binomial and polynomial and we get:
(x + 3) x (x2 + y + 5)
Step1:- Multiply each term of Binomial with polynomial keeping the addition or
subtraction sign same.
(x + 3) x (x2 + y + 5) x
= x x (x2 + y + 5) x (x2 + y + 5)
= (x x x2) + (x x y) + (x x 5) + (3 x x2) +(3 x y) + (3 x 5)
= x3 + xy + 5x x2 + 3y + 15 x
Step2:- Combine all the like terms
= x3 + 3x2 + 5x + 3y + xy (after rearranging the terms)
Ans: x3 + 3x2 + 5x + 3y + xy + 15

5. Example 2: Multiply (-5a + b) and (a + b + c) Solution:
Binomial
Polynomial
Write in the expression form product of binomial and polynomial and we get:
(-5a + b) x (a + b + c)
Step1:- Multiply each term of Binomial with polynomial keeping the addition or
subtraction sign same.
(-5a + b) x (a + b + c) x
= -5a x (a + b + c) b x (a + b + c)
= (-5a x a)+(-5a x b)+(-5a x c) + (b x a) +(b x b) + (b x c)
= - 5a2 - 5ab - 5ac ab + b2 + bc x
Step2:- Combine all the like terms
= -5a2 + b2 - 5ab + ab - 5ac + bc (after rearranging the terms)
= - 5a2 + b2 - 4ab - 5ac + bc (combining like terms)
Ans: -5a2 + b2 - 4ab - 5ac + bc

6. Example 3: Multiply (p2 + p - 6) and (p2- 6) Solution:
Binomial
Polynomial
Write in the expression form product of binomial and polynomial and we get:
(p2 - 6) x (p2 + p - 6)
Step1:- Multiply each term of Binomial with polynomial keeping the addition or
subtraction sign same.
(p2 - 6) x (p2 + p - 6) x
= p2 x (p2 + p - 6) x (p2 + p - 6)
= (p2 x p2)+(p2 x p)+(p2 x -6) + (-6 x p2) + (-6 x p) + (-6 x -6)
= p4 + p3 - 6p p2 - 6p + 36 x
Step2:- Combine all the like terms
= p4 + p3 - 6p2 - 6p2 - 6p (after rearranging the terms)
= p4 + p p2 - 6p (combining like terms)
Ans: p4 + p p2 - 6p + 36

7. Try These Multiply (- x + 4) (x2 – 2x + 8)
Multiply (xy + 7)(x2 - xy + 8)