Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Proving Polynomial Identities

Proving Polynomial Identities 1.4 - Solution

arrow_back Return to Proving Polynomial Identities
a
The difference of squares has the form (a+b)(ab)=a2b2 (a + b)(a - b) = a^2 - b^2 and we see that our expression has the same form, with a=xa = x and b=9.b = 9.
(x+9)(x9)(x + 9)(x - 9)
x292x^2 - 9^2
x281x^2 - 81
b
We proceed in the same way as in the previous part to rewrite the expression using the difference of squares.
(4+y)(4y)(4 + y)(4 - y)
42y24^2 - y^2
16y216 - y^2
c
Here, the terms are not placed in the same order inside the parentheses. However, if we change the order of the terms in (a+7)(a+7), they do!
(7a)(a+7)(7 - a)(a + 7)
(7a)(7+a)(7 - a)(7 + a)
72a27^2 - a^2
49a249 - a^2