Math, asked by spamhere447, 9 months ago

a solved example for a polynomial multiplication

Answers

Answered by abhaypratapsinghabc
4

Answer:

I sure that it will help you.

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Answered by rohitpundir066
2

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

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