Question

Pleases answer the below paper attached as I could not find the answers

Answer 1

Algebraic expressions are expressions that use variables and combination of terms.

How to determine the equivalent expressions

1. Addition

The addition expression is:

$5x^2 - \frac 13x + \frac 52 - \frac 12x^2 + \frac 12x - \frac 13 -2x^2 + \frac 15x - \frac 16$

Collect like terms

$5x^2 - \frac 12x^2 -2x^2 - \frac 13x + \frac 12x + \frac 15x + \frac 52 - \frac 13 - \frac 16$

Evaluate the like terms

$\frac 52x^2 + \frac{11}{30}x + 2$

2. Subtraction

The subtraction expression is:

$7x^2 -2x + 10 - (-2x^2 + \frac 12x - 3)$

Open the bracket

$7x^2 -2x + 10 + 2x^2 - \frac 12x +3$

Collect like terms

$7x^2 + 2x^2 -2x - \frac 12x+ 10 +3$

Evaluate the like terms

$9x^2- \frac 52x+ 13$

3. Simplify

The expression is given as:

$(\frac 13x^2 - \frac 47x + 11) - (\frac 17x - 3 -2x^2) - (\frac 27x - \frac 23x^2 + 2)$

Rewrite as:

$(\frac 13x^2 - \frac 47x + 11) - ( -2x^2 + \frac 17x - 3) - (- \frac 23x^2 + \frac 27x + 2)$

Open the brackets

$\frac 13x^2 - \frac 47x + 11 + 2x^2 - \frac 17x + 3+ \frac 23x^2 - \frac 27x - 2$

Collect like terms

$\frac 13x^2 + 2x^2 + \frac 23x^2 - \frac 47x - \frac 17x - \frac 27x + 11 + 3 - 2$

Evaluate the like terms

$3x^2 - x + 12$

4. Products

The expression is given as:

$(x-\frac 1x)(x + \frac 1x)(x^2 + \frac 1{x^2})(x^4 + \frac 1{x^4})$

Apply the difference of two squares

$(x^2-\frac 1{x^2})(x^2 + \frac 1{x^2})(x^4 + \frac 1{x^4})$

Apply the difference of two squares

$(x^4-\frac 1{x^4})(x^4 + \frac 1{x^4})$

Apply the difference of two squares

$x^8 - \frac 1{x^8}$

5. Formula

The expression is given as:

$(\frac 32m + \frac 23n)(\frac 32m - \frac 23n)$

Apply the difference of two squares

$\frac 94m^2 - \frac 49n^2$

6. Identity

The expression is given as:

$(m + 3)(m + 2)$

The identity used to solve the above expression is:

$(x + a)(x + b)$

7. Identity

The expression is given as:

$(4x + y)^2$

Expand

$16x^2 + 8xy + y^2$

Rewrite as:

$16x^2+ y^2 + 8xy$

8. Difference of two squares

The expression is given as:

$(a + b)(a - b)$

Apply the difference of two squares

$a^2 - b^2$

9. Evaluate

The expression is given as:

$a^2 + b^2$

Apply the sum of two squares

$(a + b)^2 - 2ab$

So, we have:

$5^2 - 2 * 6$

Evaluate

$13$

10. Coefficient

The expression is given as:

$\frac x2 +\frac y2 - xy$

The coefficient of xy in the expression is -1

Read more about algebraic expressions at:

brainly.com/question/4344214