Find the squares of: a) $3x + 2y$ b) $left(x – frac{1}{x}right)$

Which of the following expressions are polynomials? Write with reason.

(i) $x^2 + frac{1}{2}$

(ii) $y^2 + frac{1}{y^2}$

(iii) $sqrt{3}x – 2$

(iv) $2sqrt{x} + 5$

Find the degrees of the following polynomials.

a) $2xyz$

b) $5a^2bc$

c) $3y^2 – 4y + 8$

d) $7x^5 – 2x^4 + 5x^3 – 7x^2 – 3x$

e) $x^2 + y^2 + z^2 – 3xyz$

f) $x^3y^3 – 2x^2y^2 + 7xy – 5$

Let’s answer the following questions.

a) Why is $frac{x^2}{2}$ a polynomial but $frac{2}{x^2}$ is not a polynomial?

b) Why is $sqrt{2x}$ not a polynomial but $sqrt{2}x$ is a polynomial?

c) Define the degree of a polynomial with examples.

Let’s say and write the degrees of these polynomials.

a) $3x$ …………………

b) $2p^2$ …………………

c) $4a^2b$ …………………

d) $7y – 1$ …………………

e) $2x^3 – 3x^2 + 6$ …………………

f) $9xy – 7x + 2y$ …………………

Let’s say and write the values of the expressions as quickly as possible.

a) If $l = 4$ and $b = 3$, then (i) $l times b =$ …….. (ii) $2(l + b) =$ ……..

b) If $l = 5$, then (i) $l^2 =$ …….. (ii) $l^3 =$ …….. (iii) $6l^2 =$ ……..

Let’s say and write the polynomial expressions in the table. a) $2x + 3$

b) $3y^2 – 2y + 4$

c) $a + frac{1}{a}$

d) $sqrt{5x} + 1$

e) $frac{x^2}{2} – 3x + 7$

f) $sqrt{x + 2} – 3$

Define wave and give some examples.

Explain what do you mean by free oscillation.

What is dumped oscillation? Give an example.