Answer:
[tex]=-5x^5-5x^4+6x^3-x^2-7x+20[/tex]
OR
[tex]=-5x^5-5x^4+6x^3-x^2-7x^1+20x^0[/tex]
The above two is written in standard form:
Step-by-step explanation:
Step 1: Remove the parenthesis:
[tex](2x^{5}+x^{3}-3x^{4}-x+8)-(7x^{5}+2x^{4}-12+6x-5x^{3}+x^{2})[/tex]
[tex]=2x^5+x^3-3x^4-x+8-\left(7x^5+2x^4-12+6x-5x^3+x^2\right)[/tex]
Step 2: Focus on the equation with the parenthesis:
[tex]-\left(7x^5+2x^4-12+6x-5x^3+x^2\right)[/tex]
Step 3 and 4: Distribute the parenthesis and apply rules
[tex]-\left(-a\right)=a,\:\:\:-\left(a\right)=-a[/tex]
[tex]=-\left(7x^5\right)-\left(2x^4\right)-\left(-12\right)-\left(6x\right)-\left(-5x^3\right)-\left(x^2\right)[/tex]
[tex]=-7x^5-2x^4+12-6x+5x^3-x^2[/tex]
Step 5: Now look at the whole thing:
[tex]2x^5+x^3-3x^4-x+8-7x^5-2x^4+12-6x+5x^3-x^2[/tex]
Step 6: Move all the terms with variables to the right and constants to the right, group like terms:
[tex]=2x^5-7x^5-3x^4-2x^4+x^3+5x^3-x^2-x-6x+8+12[/tex]
Step 7: Add similar elements or terms :[tex]x^3+5x^3=6x^3[/tex]:
[tex]=2x^5-7x^5-3x^4-2x^4+6x^3-x^2-x-6x+8+12[/tex]
Step 8: Add similar elements or terms : [tex]-3x^4-2x^4=-5x^4[/tex]
[tex]=2x^5-7x^5-5x^4+6x^3-x^2-x-6x+8+12[/tex]
Step 9: Add similar elements or terms: [tex]2x^5-7x^5=-5x^5[/tex]
[tex]=-5x^5-5x^4+6x^3-x^2-x-6x+8+12[/tex]
Step 10: Add similar elements or terms: [tex]-x-6x=-7x[/tex]
[tex]=-5x^5-5x^4+6x^3-x^2-7x+8+12[/tex]
Step 11: Add similar elements or terms: [tex]8+12=20[/tex]
[tex]=-5x^5-5x^4+6x^3-x^2-7x+20[/tex]
Step 12 : ANSWER:
[tex]=-5x^5-5x^4+6x^3-x^2-7x+20[/tex]
The standard from can be written as :
[tex]=-5x^5-5x^4+6x^3-x^2-7x+20[/tex]
[tex]=-5x^5-5x^4+6x^3-x^2-7x^1+20x^0[/tex]
Why [tex]x^0[/tex] and [tex]x^1[/tex]?
If x equals 2...
Same results
That is how you order constants in standard form. Always add a constant to the 0 power with a variable to make you have a better understanding.
[tex]20=20\\20x^0=20(2)^0=20(1)=20[/tex]
[tex]-7x=-7(2)=-14\\-7x^1=-7(2)^1=-7(2)=-14[/tex]
