subtraction of polynomials

Question

trying to do the subtraction of this polynomial

 

(7 + t - 5t to the second power + 2t to the third power) - (1 + 2t - 4t to the second power + 5t to the third power)

Answer 1

(7+t-5t²+2t³)-(1+2t-4t²+5t³)

Distribute the negative

(7+t-5t²+2t³)(-1-2t+4t²-5t³)

Then combine like terms

7-1=6

t-2t=-t

-5t²+4t²=-t²

2t3-5t³=-3t³

Which leaves you having

6-t-t²-3t³

Now you can rewrite into stadard form

-3t³-t²-t+6

Answer 2

Dawn,

 

Recall that t^o is different from t¹ is different from t² is different from tn ....  And you can combine numeric coefficients ONLY within each power of t, the unknown variable. Also recall that t^o = 1 for any t, and t¹ = t. Thus, let me call the final polynomial P(t). You can rearrange it into ascending or descending powers of t:

 

P(t) = (7 + t - 5t²) + 2t³ - (1 + 2t -4t² + 5t³)

       =(7 - 1)t^o + (1 -2)t¹ + (-5 + 4)t² + (2 -5)t³

       = 6 - t - t² -3 t³

 

Also NOTICE that once the value of t becomes known, all you have left is arithmetic.  For example: P(2) = 6-2-4-3(8)=-24.

Therefore, you use Algebra when one or more variables still have unknown values, to express or compute those numeric values, then it is back to arithmetic.

Answer 3

You will first want to distribute the negative sign on the second expression.  Then, combine like terms, such as the constants, and then each of the terms containing like powers of t.  For example:

 

NOTE:  5t to the power of 3 = 5t^3

 

(3 - 4t + 5t^3) - (8 - 6t +2t^3)  

 

= 3 - 4t + 5t^3 - 8 + 6t - 2t^3   ***distribute the negative on the second expression, and drop parentheses

 

= (3-8) + (-4t + 6t) + (5t^3 - 2t^3)   ***group the like terms together

 

= -5 + 2t + 3t^3    ****finally, simplify by combining like terms

 

Now, you try it on your problem.