What letter is most commonly used to represent an unknown value or variable in algebra?
x
Simplify: 3(2d - 3) + d
Algebra: 7d - 9
What is the rule called that states you can multiply a number by a sum, like a(b + c) = ab + ac, and get the same result?
The distributive property
A letter (like x) that stands for an unknown number is called a variable.
Variable
What special name is given to the point (0,0) where the x-axis and y-axis intersect on a coordinate plane?
The origin
Simplify:
-6(6 + 5k) + 7(-k-5)
-71 - 37k
What rule states that changing the order of the numbers in an addition or multiplication problem does not change the result (e.g., a + b = b + a)?
The Commutative Property.
The number directly multiplied by a variable (like the 5 in 5x).
Coefficient
Solve: 21 = x - 17
x = 38
What is the traditional name for the rule used to expand the product of two binomials, which stands for First, Outer, Inner, Last?
FOIL method
Example
We look at the first binomials which are 4x and x which gives us 4x2
Now we look at the two outside binomials which are 4x and 3 which gives us 12x
Now we look at the two inside binomials which are 6 and x whichh gives us 6x
Now we look at the last two binomials which are 6 and 3 which gives us 18
Finally, you add all of them together to get: 4x2 +18x + 18
Q: Which mathematical law allows you to regroup numbers in an addition or multiplication equation without changing the final answer (e.g., a + (b + c) = (a + b) + c)?
The Associative Property
Must contain an equals sign (=); expressions do not.
Equation
Solve: 3x + 3 - 2x = 21
x = 18
Algebra: What is the formula for slope intercept?:
Algebra: y = mx + b
In this formula, m represents the slope (the steepness of the line) and b represents the y-intercept (the point where the line crosses the y-axis).
According to the order of operations, what must be evaluated before you perform addition or multiplication?
Parentheses and exponents must be simplified first.
A plain number that stands alone and never changes value.
Constant
Solve: 4x - 5 - 3x + 2 - 2x = 9
x = -12
If we have a polynomial equation where the highest exponent is 2 (e.g., ax² + bx + c = 0), what specific name is given to this type of equation?
A quadratic equation
Simplify: 5(2x-3)-4(x-6)
The final simplified answer is (6x + 9).
Step-by-Step Solution
What do you get if you raise any non-zero real number to the power of zero?
1
A single chunk (number, variable, or both) separated by + or - signs.
Term