Sketch and label a representation for each of the following algebraic terms. Explain how your sketches are both alike and different.
a) y^2
b) m
c) m^3
Jacqueline is making a quilt using finished squares like the one shown. Each square has an area of 310 cm^2.
a) Write an expression that represents the length of the side of the square in terms of its area.
b) Estimate the length. Describe the process you used.
c) Use a calculator to determine the correct length to two decimal places.
Determine the approximate length of the roadway bordering the adjacent square properties.
Simplify
\displaystyle
3^43^6
Simplify
\displaystyle
\frac{(\frac{4}{5})^6}{(\frac{4}{5})^5}
Simplify
\displaystyle
\frac{x^3x^6}{x}
Simplify
\displaystyle
6.1 (6.1^6)(6.1^5)(5^2)
Simplify
\displaystyle
(-7)^4(-7^6)
Simplify
a) \displaystyle
(6^3)^2
b) \displaystyle
(x^2)^5
Simplify
\displaystyle
(5x^4)^5
Simplify
\displaystyle
[(\frac{2}{5})^4]^5
Simplify
\displaystyle
(y^3)^2(y^5)^2
Simplify
\displaystyle
(\frac{2}{x^2})^2
What is meant by “like terms”? Explain how algebra tiles or diagram? can help you to identify like terms.
Simplify.
\displaystyle
5x - 2x
Simplify.
\displaystyle
7xy + 2xy
Simplify.
\displaystyle
(3x^2 -5a) + (4x^2 -a)
Which expression below is equivalent to \displaystyle
(y^2 + 5y) -(3y^2 -y)
?
A -2y^2 + 6y
B 4y^2 + 4y
C 2y^2 + 6y
D -2y^2 + 6y
E none of the above
Expand.
\displaystyle
2(x -3)
Expand.
\displaystyle
3x(4x^2 -5x)
Expand.
\displaystyle
y^5(5y^4 + 3y^3 -y^2)
Expand and simplify.
\displaystyle
2(x -3) + 3(x + 2)
Expand and simplify.
\displaystyle
3(y^2 + y -2) - (y^2 + 2y + 4)
Expand and simplify.
\displaystyle
2x(3x -2) + x^2 + 0.2(x^2 + 3)
Mary and Bill are setting up a summer concession stand at the park. They need these jobs filled:
a) Determine a simplified algebraic expression to represent the weekly payroll for all 11 employees. Assume that they will always work at least 30 h per week.
b) Use your expression to determine the weekly payroll if each employee works 32 h per week.
Determine an expression that simplifies to 3x^2 if the expression contains:
- exactly two binomials
- the distributive property used once