Question

How do i multiply polynomials (please include examples)

Answer 1

Rules for Multiplying Polynomials:

Multiplying polynomials require only three steps.

- First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.
- Add the powers of the same variables using the exponent rule.
- Then, simplify the resulting polynomial by adding or subtracting the like terms.

It should be noted that the resulting degree after multiplying two polynomials will be always more than the degree of the individual polynomials.

Example 1: Find the result of multiplication of two polynomials (6x +3y) and (2x+ 5y).

Solution- (6x−3y)×(2x+5y)

⇒6x×(2x+5y)−3y×(2x+5y) (Distributive law of multiplication)

⇒(12x^2+30xy)−(6yx+15y^2) (Distributive law of multiplication)

⇒12x^2+30xy−6xy−15y^2 (as xy = yx)

Thus, (6x+3y)×(2x+5y)=12x^2+24xy−15y^2

Example 2:

Let us take up an example. Say, you are required to multiply a binomial (5y + 3z) with another binomial (7y − 15z). Let us see how it is done.

(5y + 3z) × (7y − 15z)
= 5y × (7y − 15z) + 3z × (7y − 15z) (Distributive law of multiplication)

= (5y × 7y) − (5y × 15z) + (3z × 7y) − (3z × 15z) (Distributive law of multiplication)

= 35y^2 − 75yz + 21zy − 45z^2

= 35y^2 − 75yz + 21yz − 45z^2

As, (yz = zy)

(5y + 3z) × (7y − 15z) = 35y^2 −54yz − 45z^2

[i HOPE THIS HELPS YOU. PLEASE TELL ME IF YOU NEED MORE HELP]

Answer 2

Step 1: Arrange the polynomials in standard form: (3x + 2) * (4x - 1)

Step 2: Multiply each term: (3x 4x) + (3x -1) + (2 4x) + (2 -1) = 12x^2 - 3x + 8x - 2

Step 3: Combine like terms: = 12x^2 + 5x - 2

So, the product of (3x + 2) and (4x - 1) is 12x^2 + 5x - 2.

Remember to always double-check your calculations, especially when dealing with multiple terms.

Answer 3

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