Answer:
[tex]6x^2 -x - 1[/tex]
By degree: Quadratic
By number of terms: Trinomial
[tex]3x + 4[/tex]
By degree: Linear
By number of terms: Binomial
[tex]2[/tex]
By degree: Constant
By number of terms: Monomial
Step-by-step explanation:
Given
[tex](x - \frac{1}{2})(6x + 2)[/tex]
[tex](7x^2 + 3x) -\frac{1}{3}(21x^2 - 12)[/tex]
[tex]4(5x^2-9x+7)+2(-10x^2+18x-13)[/tex]
Required
Simplify and categorize the result based on their degree and number of terms
Simplifying [tex](x - \frac{1}{2})(6x + 2)[/tex]
[tex]x(6x + 2) - \frac{1}{2}(6x + 2)[/tex]
Open bracket
[tex]6x^2 + 2x - 3x - 1[/tex]
[tex]6x^2 -x - 1[/tex]
By degree: Quadratic
By number of terms: Trinomial
Simplifying [tex](7x^2 + 3x) -\frac{1}{3}(21x^2 - 12)[/tex]
Open bracket
[tex]7x^2 + 3x -\frac{1}{3} * 21x^2 -\frac{1}{3}*- 12[/tex]
[tex]7x^2 + 3x -7x^2 + 4[/tex]
Collect like terms
[tex]7x^2-7x^2 + 3x + 4[/tex]
[tex]3x + 4[/tex]
By degree: Linear
By number of terms: Binomial
Simplifying [tex]4(5x^2-9x+7)+2(-10x^2+18x-13)[/tex]
Open brackets
[tex]4*5x^2-4*9x+4*7+2*-10x^2+2*18x-2*13[/tex]
[tex]20x^2-36x+28-20x^2+36x-26[/tex]
Collect like terms
[tex]20x^2-20x^2-36x+36x+28-26[/tex]
[tex]2[/tex]
By degree: Constant
By number of terms: Monomial
