Exercises

1. Match the like terms from Column 1 with the like terms in Column 2.

   Column 1

   1. \(7d^2\)
   2. \(13d^9f^3\)
   3. \(40f^5\)
   4. \(-6d^3f^2\)
   5. \(9f^4d\)
   6. \(5d^2f^7\)
   7. \(f^2\)

   Column 2

   1. \(3f^7d^2\)
   2. \(-17f^5\)
   3. \(100f^2\)
   4. \(\frac{21}{2}df^4\)
   5. \(-9d^2\)
   6. \(f^2d^3\)
   7. \(-2f^3d^9\)
2. Simplify.
   1. \(3x^2-4x+22+9x^2+4x-14\)
   2. \(7a^2-b^3+9a^2+20+12b^3\)
   3. \(13xy+6x-8y+20-2xy+13-9x+13y\)
   4. \((5y^3-y^2+8y)-(3y^3-7y^2+10y)\)
   5. \((-3d^3-6d)+(-2d^3-5d^2+11)\)
   6. \((12+4p^2-11p)-(6p^3-15)\)
3. Find the unknown expression (represented by \(?\)).
   1. \((7x^2-5x-3)+(?)=-9x^2+2x-8\)
   2. \((?)-(-9x^2+6x-3)=4x^2+4x-6\)
   3. \((6x^2+7)-(?)=x^2+x+2\)
   4. \(-(?)+(6x^2+x-5)=15x^2+1\)
4. The side length of a regular pentagon is represented by the expression \(12a-3\).
   1. Write an expression to represent the perimeter of the pentagon.
   2. If \(a=2\) cm, what is the perimeter of the pentagon? 
5. Determine:
   1. three polynomials that have a sum of \(18a^2b^2+13a-4b+6\).
   2. two polynomials with a difference of \(5x^3-7x^2+12x\).
6. The sequence \(1,~1,~2,~3,~5,~8,...\) is called the Fibonacci sequence, and with the exception of the first two terms, each succeeding term is the sum of the two previous terms. Suppose that the first two terms of a new Fibonacci sequence are represented by the expressions \(n\) and \(n+5\). Determine:
   1. the expression representing the \(7\)^th term.
   2. an expression representing the sum of the first \(6\) terms.
7. Octavia simplified the polynomial \(6a+3\) to \(9a\). Is she correct? Explain your answer.
8. Each row, column, and diagonal have a sum of \(15n+15\). Determine an expression to represent the value of \(z-v+w-x-y\).

   \(8n+4\)	\(x\)	\(y\)
   \(w\)	\(5n+5\)	\(7n+1\)
   \(z\)	\(9n+7\)	\(v\)