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Study Guide: Algebra-II
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Algebra-II

By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.

⏱️ ~2 min read
Algebraic Formulas:

1. Binomial Theorem:
(a+b)0=1
(a+b)1=a+b
(a+b)2=a2+2ab+b2
(a-b)2=a2-2ab+b2
(a+b)3=a3+3a2b+3ab2+b3
(a-b)3=a3-3a2b+3ab2-b3
(a+b)4=a4+4a3b+6a2b2+4ab3+b4

2. Difference of Two Squares Formula:
x2 - y2=(x+y)(x - y)

3. Sum / Difference of Two Cubes:
x3+y3=(x+y)(x2 - xy+y2)
x3’y3=(x- y)(x2+xy+y2)


Example:1
Evaluate:
(x+3)2
Using the formula for a perfect square: (a+b)2=a2+2ab+b2
=>
(x+3)2=x2+2(x)(3)+(3)2
=>
(x+3)2=x2+6x+9

Example 2:
Evaluate:
(2x - 6)2
Using the formula for binomial difference squared:
(a - b)2=a2 - 2ab+b2
=>
(2x - 6)2=(2x)%2 - 2(2x)(6)+(6)2(2x-6)2=(2x)2-2(2x)(6)+(6)2
=>
(2x - 6)2=4x2 - 24x+36(2x-6)2=4x2-24x+36

Example 3:
Evaluate:
(2x - 5)3
Using the binomial theorem for cube
(a - b)3=a3 - 3a2b+3ab2 - b3
=>
(2x - 5)3=(2x)3 - 3(2x)2(5)+3(2x)(5)2 - (5)3
=>
(2x - 5)3=8x3 - 3(4x2)(5)+3(2x)(25) - 125
=>
(2x - 5)3=8x3 - 60x2+150x - 8

Example 4:
Evaluate:
(2x+5)(2x - 5)
From the Difference of the Squares Formula, we know that
a2 - b2=(a+b)(a - b)
=>
(2x+5)(2x - 5)=(2x)2 - (5)2
=>
(2x+5)(2x - 5)=4x2 - 25

Example 5:
Factorize:
x3+64
We can express the given expression as the sum of cubes form:
x3+64=x3+(4)3
=>
x3+64=(x+4)[x2 - (x)(4)+(4)2]
=>
x3+64=(x+4)(x2 - 4x+ 16)

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