Algebraic expressions are expressions that use variables and combination of terms.
1. Addition
The addition expression is:
[tex]5x^2 - \frac 13x + \frac 52 - \frac 12x^2 + \frac 12x - \frac 13 -2x^2 + \frac 15x - \frac 16[/tex]
Collect like terms
[tex]5x^2 - \frac 12x^2 -2x^2 - \frac 13x + \frac 12x + \frac 15x + \frac 52 - \frac 13 - \frac 16[/tex]
Evaluate the like terms
[tex]\frac 52x^2 + \frac{11}{30}x + 2[/tex]
2. Subtraction
The subtraction expression is:
[tex]7x^2 -2x + 10 - (-2x^2 + \frac 12x - 3)[/tex]
Open the bracket
[tex]7x^2 -2x + 10 + 2x^2 - \frac 12x +3[/tex]
Collect like terms
[tex]7x^2 + 2x^2 -2x - \frac 12x+ 10 +3[/tex]
Evaluate the like terms
[tex]9x^2- \frac 52x+ 13[/tex]
3. Simplify
The expression is given as:
[tex](\frac 13x^2 - \frac 47x + 11) - (\frac 17x - 3 -2x^2) - (\frac 27x - \frac 23x^2 + 2)[/tex]
Rewrite as:
[tex](\frac 13x^2 - \frac 47x + 11) - ( -2x^2 + \frac 17x - 3) - (- \frac 23x^2 + \frac 27x + 2)[/tex]
Open the brackets
[tex]\frac 13x^2 - \frac 47x + 11 + 2x^2 - \frac 17x + 3+ \frac 23x^2 - \frac 27x - 2[/tex]
Collect like terms
[tex]\frac 13x^2 + 2x^2 + \frac 23x^2 - \frac 47x - \frac 17x - \frac 27x + 11 + 3 - 2[/tex]
Evaluate the like terms
[tex]3x^2 - x + 12[/tex]
4. Products
The expression is given as:
[tex](x-\frac 1x)(x + \frac 1x)(x^2 + \frac 1{x^2})(x^4 + \frac 1{x^4})[/tex]
Apply the difference of two squares
[tex](x^2-\frac 1{x^2})(x^2 + \frac 1{x^2})(x^4 + \frac 1{x^4})[/tex]
Apply the difference of two squares
[tex](x^4-\frac 1{x^4})(x^4 + \frac 1{x^4})[/tex]
Apply the difference of two squares
[tex]x^8 - \frac 1{x^8}[/tex]
5. Formula
The expression is given as:
[tex](\frac 32m + \frac 23n)(\frac 32m - \frac 23n)[/tex]
Apply the difference of two squares
[tex]\frac 94m^2 - \frac 49n^2[/tex]
6. Identity
The expression is given as:
[tex](m + 3)(m + 2)[/tex]
The identity used to solve the above expression is:
[tex](x + a)(x + b)[/tex]
7. Identity
The expression is given as:
[tex](4x + y)^2[/tex]
Expand
[tex]16x^2 + 8xy + y^2[/tex]
Rewrite as:
[tex]16x^2+ y^2 + 8xy[/tex]
8. Difference of two squares
The expression is given as:
[tex](a + b)(a - b)[/tex]
Apply the difference of two squares
[tex]a^2 - b^2[/tex]
9. Evaluate
The expression is given as:
[tex]a^2 + b^2[/tex]
Apply the sum of two squares
[tex](a + b)^2 - 2ab[/tex]
So, we have:
[tex]5^2 - 2 * 6[/tex]
Evaluate
[tex]13[/tex]
10. Coefficient
The expression is given as:
[tex]\frac x2 +\frac y2 - xy[/tex]
The coefficient of xy in the expression is -1
Read more about algebraic expressions at:
https://brainly.com/question/4344214
