Question

Solve the question given above

Chapter : Algebra

Please write step by step explanation
please.. yarr

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Answer 1

Question:

Multiply:

$\sf\:\dfrac{xy}{2}\:\times\:\left(\:4x\:-\:\dfrac{2}{5}\:y^2x\:\right)$

Answer:

$\boxed{\red{\sf\:\dfrac{xy}{2}\:\times\:\left(\:4x\:-\:\dfrac{2}{5}\:y^2x\:\right)\:=\:\dfrac{10\:x^2y\:-\:x^2\:y^3}{5}}}$

Step-by-step-explanation:

We have given two algebraic polynomials.

We have to find the product of those two polynomials.

$\sf\:\dfrac{xy}{2}\:\times\:\left(\:4x\:-\:\dfrac{2}{5}\:y^2x\:\right)$

$\implies\sf\:\dfrac{xy}{2}\:\times\:\left(\:4x\:-\:\dfrac{2}{5}\:xy^2\:\right)$

$\implies\sf\:\dfrac{xy}{2}\:\times\:\left(\:\dfrac{20x\:-\:2xy^2}{5}\:\right)$

$\implies\sf\:\dfrac{xy}{2}\:\times\:\dfrac{20x\:-\:2xy^2}{5}$

$\implies\sf\dfrac{20\:x^2y\:-\:2\:x^2\:y^3}{10}\:\:-\:-\:[\:\because\:a^m\:\times\:a^n\:=\:a^{m\:+\:n}\:]$

Dividing each term by 2, we get,

$\implies\sf\:\dfrac{10\:x^2y\:-\:x^2\:y^3}{5}$

$\therefore\:\boxed{\red{\sf\:\dfrac{xy}{2}\:\times\:\left(\:4x\:-\:\dfrac{2}{5}\:y^2x\:\right)\:=\:\dfrac{10\:x^2y\:-\:x^2\:y^3}{5}}}$

$\rule{200}{1}$

Additional Information:

1. Polynomial:

Any mathematical expression which contains numbers and letters is called as a polynomial.

2. Constant terms:

Every number is a constant term.

The value of any constant term never changes.

3. Variables:

The letters used in making polynomials and mathematical expressions are called as variables.

As they vary in every example, expression, they are known as vari - ables [ One which is able to vary anytime ].

4. Kinds of polynomials:

There are two main kinds of polynomials:

1. Term polynomial

2. Degree polynomial

5. Term polynomial:

There are basically three types of term polynomial:

A. Monomial ( Only one term )

B. Binomial ( Two terms )

C. Trinomial ( Three terms )

6. Degree polynomial:

There are basically four types of degree polynomial:

A. Linear polynomial ( Degree is 1 )

B. Quadratic Polynomial ( Degree is 2 )

C. Cubic Polynomial ( Degree is 3 )

D. Biquadratic polynomial ( Degree is 4 )