Polynomial product
Introduction:
Algebra is a subdivision in mathematics in which comprises of infinite number of operations on equations, polynomials, inequalities, radicals, rational numbers, logarithms, etc. Polynomials are expressions which has terms with combination of variables and constants. These terms are combined with arithmetic operators. Arithmetic operations are performed with polynomials like addition , subtraction, multiplication and division. The brief explanation about polynomials product with examples are illustrated below.
Procedure for polynomial product:
The following steps are essential to do product of polynomials,
Case 1: If a number or term say 'x' has to be multiplied with a polynomial.
Step 1: Multiply the term to be multiplied say 'x' with every term in the polynomial.
Step 2: Follow the rule for sign change while multiplying. And also the exponents rule
Step 3: Add the powers if necessary.
Step 4: Then do the operations say '+' or '-' as intended to obtain the answers.
Case 2: If a polynomial of 'n' terms has to be multiplied with another polynomial of 'm' terms.
Step 1: Take the first term in polynomial one and multiply it with every term in the second polynomial
Step 2: Follow the rule for sign change while multiplying. And also the exponents rule
Step 3: Take the second term in polynomial one and multiply it with every term in the second polynomial
Step 4: Follow the rule for sign change while multiplying. And also the exponents rule.
Step 5: Follow the above procedure, for all terms in polynomial 1.
Step 6: Then group them to obtain the answers.
Example To find the product:
Problem 1:
Find the product of (6a) and (3x2 + 4x + 6).
Solution:
Multiply the term to be '6a' with every term in the polynomial.
6a(3x2) + 6a(4x) +6a(6),
18x2 a + 24ax + 36a
Example 2:
Find the product of the polynomials (7x2 – x – 5) and (x2 – 2x – 4)
Solution:
Step 1: Take the first term in polynomial one and multiply it with every term in the second polynomial, do the same for all the terms in polynomial 1
Therefore,
= 7x2 (x2 ) + 7x2 (-2x) +7x2 (-4) +(-x)(x2 ) +(-x) (-2x) + (-x)(-4) + (-5) (x2 ) + (-5)(-2x) + (-5)(-4)
=7x4 -14x3 -28x2 - (x3 ) + (2x2) + 4x -5 (x2 ) + 10x +20
Adding like terms,
=7x4 -14x3 - (x3 ) -28x2 + (2x2) - 5 (x2 ) + 4x + 10x +20.
=7x4 -15x3 -31x2 + 16x +20.
Example 3:
Find the product of the polynomials (2x +x2 ) and (4x + x3 )
Solution:
Step 1: Take the first term in polynomial one and multiply it with every term in the second polynomial, do the same for all the terms in polynomial 1
2x (4x) + 2x (x3 ) + x2(4x) + x2 (x3)
8(x)(x) + 2(x) (x3) + 4(x) (x2) + (x2 ) (x3)
Use the exponents rule,( am *an = am+n)
8x2 + 2x4 + 4x3 + x5
I like to share this Polynomial Functions Examples and Multiplying Polynomials with you all through my blog.
Algebra is a subdivision in mathematics in which comprises of infinite number of operations on equations, polynomials, inequalities, radicals, rational numbers, logarithms, etc. Polynomials are expressions which has terms with combination of variables and constants. These terms are combined with arithmetic operators. Arithmetic operations are performed with polynomials like addition , subtraction, multiplication and division. The brief explanation about polynomials product with examples are illustrated below.
Procedure for polynomial product:
The following steps are essential to do product of polynomials,
Case 1: If a number or term say 'x' has to be multiplied with a polynomial.
Step 1: Multiply the term to be multiplied say 'x' with every term in the polynomial.
Step 2: Follow the rule for sign change while multiplying. And also the exponents rule
Step 3: Add the powers if necessary.
Step 4: Then do the operations say '+' or '-' as intended to obtain the answers.
Case 2: If a polynomial of 'n' terms has to be multiplied with another polynomial of 'm' terms.
Step 1: Take the first term in polynomial one and multiply it with every term in the second polynomial
Step 2: Follow the rule for sign change while multiplying. And also the exponents rule
Step 3: Take the second term in polynomial one and multiply it with every term in the second polynomial
Step 4: Follow the rule for sign change while multiplying. And also the exponents rule.
Step 5: Follow the above procedure, for all terms in polynomial 1.
Step 6: Then group them to obtain the answers.
Example To find the product:
Problem 1:
Find the product of (6a) and (3x2 + 4x + 6).
Solution:
Multiply the term to be '6a' with every term in the polynomial.
6a(3x2) + 6a(4x) +6a(6),
18x2 a + 24ax + 36a
Example 2:
Find the product of the polynomials (7x2 – x – 5) and (x2 – 2x – 4)
Solution:
Step 1: Take the first term in polynomial one and multiply it with every term in the second polynomial, do the same for all the terms in polynomial 1
Therefore,
= 7x2 (x2 ) + 7x2 (-2x) +7x2 (-4) +(-x)(x2 ) +(-x) (-2x) + (-x)(-4) + (-5) (x2 ) + (-5)(-2x) + (-5)(-4)
=7x4 -14x3 -28x2 - (x3 ) + (2x2) + 4x -5 (x2 ) + 10x +20
Adding like terms,
=7x4 -14x3 - (x3 ) -28x2 + (2x2) - 5 (x2 ) + 4x + 10x +20.
=7x4 -15x3 -31x2 + 16x +20.
Example 3:
Find the product of the polynomials (2x +x2 ) and (4x + x3 )
Solution:
Step 1: Take the first term in polynomial one and multiply it with every term in the second polynomial, do the same for all the terms in polynomial 1
2x (4x) + 2x (x3 ) + x2(4x) + x2 (x3)
8(x)(x) + 2(x) (x3) + 4(x) (x2) + (x2 ) (x3)
Use the exponents rule,( am *an = am+n)
8x2 + 2x4 + 4x3 + x5
I like to share this Polynomial Functions Examples and Multiplying Polynomials with you all through my blog.