This document contains 6 math exercises involving polynomial expressions and identities: 1) Expanding binomial expressions. 2) Expanding the binomial (xx + yy)88. 3) Identifying the nth power and binomial of the expression 2277xx66 − 113333xx44 + 222222xx22 − 111111. 4) Expanding polynomial expressions. 5) Finding the polynomial identity that gives the expression 44xx22 − 1111yy22. 6) Finding the polynomial identity that gives the expression − 22yy + 1111xx22 + xx22yy22.

1. UNIT 03 December
1. Solve:
a) (𝒙𝒙 + 𝟑𝟑)𝟐𝟐
=
b) ( 𝟑𝟑𝒙𝒙 − 𝟓𝟓)𝟐𝟐
=
c) (𝒙𝒙 + 𝟐𝟐𝟐𝟐)𝟑𝟑
=
d) (𝒙𝒙 − 𝟐𝟐)𝟒𝟒
=
e) ( 𝟐𝟐𝒙𝒙 − 𝒚𝒚)𝟒𝟒
=
f) ( 𝟑𝟑𝟑𝟑 − 𝒙𝒙)𝟓𝟓
=
2. Do (𝒙𝒙 + 𝒚𝒚)𝟖𝟖
.
3. The nth power of a binomial is 𝟐𝟐𝟕𝟕𝒙𝒙𝟔𝟔
− 𝟏𝟏𝟑𝟑𝟑𝟑𝒙𝒙𝟒𝟒
+ 𝟐𝟐𝟐𝟐𝟐𝟐𝒙𝒙𝟐𝟐
− 𝟏𝟏𝟏𝟏𝟏𝟏. Which is n?
Which is the binomial?
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.2.1

2. UNIT 03 December
4. Solve these polynomial identities:
a) (𝒙𝒙 + 𝟑𝟑𝒚𝒚)𝟐𝟐
=
b) ( 𝟑𝟑𝒙𝒙 + 𝟐𝟐)( 𝟑𝟑𝟑𝟑 − 𝟐𝟐) =
c) ( 𝟓𝟓𝒙𝒙 − 𝟏𝟏)𝟐𝟐
=
d) (𝒙𝒙 + 𝟓𝟓𝟓𝟓)(𝒙𝒙 − 𝟓𝟓𝟓𝟓) =
e) (−𝟑𝟑𝟑𝟑 + 𝒚𝒚)𝟐𝟐
=
f) (−𝟐𝟐𝟐𝟐 − 𝒚𝒚)𝟐𝟐
=
5. Find the polynomial identity that gives 𝟒𝟒𝒙𝒙𝟐𝟐
− 𝟏𝟏𝟏𝟏𝒚𝒚𝟐𝟐
:
6. Find the polynomial identity that gives
−
𝟐𝟐
𝒚𝒚
+
𝟏𝟏
𝒙𝒙𝟐𝟐
+
𝒙𝒙𝟐𝟐
𝒚𝒚𝟐𝟐
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.3.2.2