Download NAME: DATE: ______ Algebra 2: Lesson 2

NAME: ______________________________________________________
DATE: _____________
Algebra 2: Lesson 2-4 Structure and Factoring
Learning Goals:
1) How can we use factoring to change the structure of an expression?
Warm-Up
Show that (
)
How could we show (
(
)
)
for all real numbers
(
)
and .
using the difference of two squares property?
We can use the difference of two squares property to rewrite expressions and view them in a different
form that can be more useful to us.
1) Rewrite each expression as a sum or difference of terms:
To solve these we could write
out the expression, double
distribute, and combine like
terms; but that would take a
long time! We can use the
difference of two squares
property to help us simplify
this process.
a) ( x  y) 2 ( x  y) 2
b) ( x  y) 2 ( x 2  y 2 ) 2 ( x  y) 2
)(
)
2) Show that the expression (
squares and then factor the expression.
may be written as the difference of two
3) Factor the following expression completely: x2 + 4x + 4 – 9y2
4) Tasha used a clever method to expand and simplify (
)(
). She grouped the
)
][(
)
addends together like this [(
] and then expanded them to get the
difference of two squares:
(
)(
)
[(
)
][(
)
]
(
)
a) Is Tasha's method correct? Explain why or why not.
b) Use a version of her method to find (
)(
).
c) Use a version of her method to find (
)(
).
5) Consider the polynomial expression
a) Is
.
factorable using the methods we have seen so far?
b) Factor
first as a difference of cubes, then factor completely: (
c) Factor
first as a difference of squares, then factor completely: (
d) Explain how your answers to parts (b) and (c) provide a factorization of
)
.
)
.
e) If a polynomial can be factored as either a difference of squares or a difference of cubes, which
formula should you apply first, and why?
Let’s use factoring to change the structure of other types of expressions…
6) Use the properties of exponents to verify that the following are true.
4 n2  4 n
 5  4n
a)
3
n1
n2
n1
b) 4  4  5  4