Writing Algebraic Expressions
Write an expression for 3 less than twice x.
2x - 3
Name two ways to multiply binomials
double distribute
and
box method / area model
We can tell expressions are equivalent when ...
they evaluate to the same value given the same value of the variable.
Evaluate the expression x + 4 for x = 10.
14
To simplify expressions, we combine ...
Like terms
Pencils are sold in packages of 12. How would you write an expression for the total number of pencils in p packages?
12p
Write a trinomial expression in standard form that is equivalent to (x + 8)(x + 3)
x2 + 11x + 24
Simplify the expressions to see if they are equivalent.
6(n + 2) and 12 + 6n
Yes, they are equivalent.
Evaluate the expression (20/n) - 2 when n = 5
2
Simplify the expression
2n + 5 + b - n + 3.
n + 8 + b
Write expressions for each of the following.
(a) Twice the sum of n and 5.
(b) The sum of twice n and 5.
(a) 2(n+5)
(b) 2n + 5
Write a trinomial expression in standard form that is equivalent to (2x + 5)(3x - 2)
6x2 + 11x - 10
Use the commutative property of addition to write an equivalent expression.
x + 7
7 + x
Evaluate the expression 3x-24 for x = 5.
- 9
Like terms have these two things in common
The same variables with the same exponents
The quotient of the sum of three more than two times a number n, and the difference of four and the number n.
(2n+3)/(n-4)
Find the trinomial that is equivalent to (x + 2)2.
(x + 2)2 = (x + 2)(x + 2)
= x2 + 4x + 4
Distribute and simplify to find an equivalent expression.
2(n+5) + (3n - 7)
2n+10+3n-7=
5n + 3
Evaluate the expression x2 - 3x when x = - 2.
10
Write an equivalent expression for
4x2 + x + 4 + 23 + x
by combining like terms
4x2 + 2x + 12
Francisco is five years more than twice Jenna's age. If Jenna's age is given by a, then write expressions for Francisco's age and the sum of their ages, in terms of a.
Francisco's age: 2a + 5
Sum of their ages: a + 2a + 5
= 3a + 5
Rewrite the expression below as an equivalent product of two binomials.
(x - 8)(4x + 5) - (x - 8)(2x - 4)
(x - 8)((4x + 5) - (2x - 4))
= (x - 8)(4x + 5 - 2x + 4)
= (x - 8)(2x + 9)
Distribute and simplify to find an equivalent expression.
-2x(x + 7) - 3x(4x - 6)
-2x(x + 7) - 3x(4x - 6)
-4x2 - 14x -12x2 + 18x
-16x2 + 4x
Evaluate the expression 5(x2 - 11) when x is -3.
-10
Write the following expression in simplest binomial form.
4(3x - 2) - 2(4x + 5)
4x - 18