a solved example for a polynomial multiplication
Answers
Answer:
I sure that it will help you.
Step-by-step explanation:
Polynomial multiplication is a very common operation throughout Algebra and Mathematics in general. We use following three properties very frequently all the way along as we work on multiplication of polynomials.
Associative Properties of Algebra
Distributive Properties of Algebrat
Commutative Properties of Algebra
Rules / Laws of Exponents
We have already discussed the first three properties in the preceding topics.
We enlist the relevant formulas below so that you can revise these properties quickly:
Commutative Law For Addition
a+b=b+a
Commutative Law For Multiplication
a⋅b=b⋅a
Associative Law For Addition
a+(b+c)=(a+b)+c
Associative Law For Multiplication
a⋅(b⋅c)=(a⋅b)⋅c
Distributive Law
a⋅(b+c)=(a⋅b)+(a⋅c)
Exponent Rule Example
Example 1:
Use rules of Exponents to simplify the following algebraic expression:
Note:
These are some of the most basic rules for polynomial multiplication. Now that you have practiced these simplifications, the process of multiplication is going to be very easy for you
The simple rule that we use while multiplying two polynomials is that
We multiply each term of the first polynomial by each term of the second polynomial and thereafter combine the like terms. The result is also a polynomial.
While multiplying these terms, we make use of the rules of exponents stated above, whereas the remaining formulas help us simplify and / or expand the multiplying polynomials.
We start with the simpler examples (involving monomials) and then proceed towards more complex examples (those involving polynomials with 2 and more terms).
Polynomial Multiplication Examples
find the product:
(4x²) (-3x⁴)
= (4x²) (-3x⁴)
=(4)(-3) (x² +⁴)
= -12x6 -------------- x square mai hai 6
find the product:
(2x)(4x² + 3xy)
= (2x) (4x² + 3xy)
=(2x) (4x²) + (2x) (3xy)
= (2)(4) (x.x²) + (2)(3)(x.xy)
= 8x¹+² + 6x¹+¹y
= 8x³ + 6x²y