Use algebra to express each situation. Write an algebraic expression to represent the model.

a) Jeanne ran 4 km.

b) Klaus drove an unknown distance, twice.

c) Evelyn ran 3 km plus an unknown distance.

d) Suki painted her house with two coats of paint.

a) Build a volume model to represent a cube with side length 3 cm. Sketch the model and label the length, width, and height.

b) What is the volume of the cube? Write this as a power.

c) Write an expression for the area of one face of the cube as a power. Evaluate the area of one face.

Evaluate

a) \displaystyle 4^5

b) \displaystyle (-3)^4

c) \displaystyle (\frac{2}{5})^3

d) \displaystyle 1.05^8

$100 is put into a bank account that pays interest so that the amount in the account grows according to the expression 100(1.06)n, where n is the number of years. Find the amount in the account after

a) 5 years

b) 10 years

The half-life of carbon-14 (C-14) is 5700 years.

a) Copy and complete the table for a 50-g sample of C-14.

b) Construct a graph of the amount of C-14 remaining versus time, in years. Describe the shape of the graph.

c) Approximately how much C-14 will remain after 20 000 years?

d) How long will it take until only 1 g of C-14 remains?

Write it as a single power.

\displaystyle 2^3 \times 2^2 \times 2^4

Write it as a single power.

\displaystyle 6^7 \div 6^2 \div 6^3

Write it as a single power.

\displaystyle [(-4)^2]^3

Write it as a single power.

\displaystyle \frac{7^4 \times 7^5}{(7^4)^2}

Simplify

\displaystyle \frac{n^5 \times n^3}{n^4}

Simplify

\displaystyle cd^3 \times c^4 d^2

Simplify

\displaystyle \frac{2ab^2 \times 3a^3b^3}{(4ab^2)^2}

Identify the coefficient and the variable part of each term.

a) \displaystyle 5y

b) \displaystyle uv

c) \displaystyle \frac{1}{2}ab^2

d) \displaystyle -de^2f

e) \displaystyle 8

f) \displaystyle 16 i^2 -7v^2

Classify each polynomial by the number of terms.

a) \displaystyle x^2 + 3x - 5

b) \displaystyle 24xy

c) \displaystyle a + 2b - c + 3

d) \displaystyle - \frac{2}{3}

e) \displaystyle 16u^2 -7v^2

In a hockey tournament, teams are awarded 3 points for a win, 2 points for an overtime win, and 1 point for an overtime loss.

a) Write an expression that describes the number of points a team has.

b) Use your expression to find the number of points earned by a team that has 4 wins, 1 overtime win, and 2 overtime losses.

State the degree of each term.

a) \displaystyle 3x^2

b) \displaystyle 6n^4

c) \displaystyle 17

d) \displaystyle abc^2

State the degree of each polynomial.

a) \displaystyle 3y - 5

b) \displaystyle 2d^2 -d

c) \displaystyle 3w -6w^2 + 4

d) \displaystyle 3x^3 -5x^2 + x

Identify the like terms in each set.

a) \displaystyle 2p, 3q, -2, p, 3q^2

Identify the like terms in each set.

a) \displaystyle 5x^2, 5x , x^5, -5x^2, 3x^2

Simplify by collecting like terms.

a) \displaystyle 4x - 3 + 6x + 5

b) \displaystyle 7k + 5m -k - 6m

Simplify by collecting like terms.

\displaystyle 6a^2 - 5a + 3 - 3a^2 + 5a -4

Simplify by collecting like terms.

\displaystyle 3x^2 - 4xy + 5y^2 - 6 + 3x^2+ 4xy -2

Simplify

a) \displaystyle (4x +3) + (3x - 2)

b) \displaystyle (5k -2) + (3k - 5)

c) \displaystyle (6u+1) - (2u + 5)

Simplify

\displaystyle (y^2 -3y)-(2y^2 - 5y)

Simplify

\displaystyle (2a^2 -4a -2)-(a^2 -4a + 2)

Simplify

\displaystyle (3v -2)-(v-3)+(2v - 7)

A rectangular window frame has dimensions expressed by 3x and 2x - 5. Find a simplified expression for its perimeter.

Expand.

a) \displaystyle 3(y - 7)

b) \displaystyle -2(x + 3)

c) \displaystyle m(5m -3)

d) \displaystyle -4k(2k + 6)

Expand.

a) \displaystyle -5(p^2 + 3p - 1)

b) \displaystyle 4b(b^2 - 2b + 5)

Expand and simplify.

a) \displaystyle 2(q - 5) + 4(3q +2)

b) \displaystyle 5x(2x -4) -3(2x^2 +8)

Expand and simplify.

a) \displaystyle -3(2m - 6) - (8 - 6m)

b) \displaystyle 4(2d-5) + 3(d^2 -3d) -2d(d+ 1)

Simplify

\displaystyle 2[4 + 3(x - 5)]

Simplify

\displaystyle -3[9 - 2(k + 3)+ 5k]