Multiplying binomial with polynomial

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Presentation transcript:

Multiplying binomial with polynomial

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

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

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) + 3 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 + 3x2 + 3y + 15 x Step2:- Combine all the like terms = x3 + 3x2 + 5x + 3y + xy + 15 (after rearranging the terms) Ans: x3 + 3x2 + 5x + 3y + xy + 15

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

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) + -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 - 6p2 - 6p2 - 6p + 36 x Step2:- Combine all the like terms = p4 + p3 - 6p2 - 6p2 - 6p + 36 (after rearranging the terms) = p4 + p3 - 12 p2 - 6p + 36 (combining like terms) Ans: p4 + p3 - 12 p2 - 6p + 36

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