Test your understanding of the algebraic proof of:

\(a^2 – b^2 = (a+b)(a-b)\)

Try to answer the questions before checking the answers at the bottom of the page.

Question 1

Which identity is correct?

A) \(a^2−b^2=(a+b)(a−b)\)

B) \(a^2−b^2=(a−b)^2\)

C) \(a^2−b^2=a+b\)

Question 2

Expand:

\((x+4)(x−4)\)

A) \(x^2−8x+16\)

B) \(x^2−16\)

C) \(x^2+16\)

Question 3

Which terms cancel in:

\(a^2−ab+ab−b^2\)

A) \(a^2\) and \(b^2\)

B) \(−ab\) and \(ab\)

C) \(a^2\) and \(ab\)

Question 4

Simplify:

\((y+7)(y−7)\)

A) \(y^2−49\)

B) \(y^2+49\)

C) \(y^2−14y+49\)

Question 5

Evaluate:

\(12^2−2^2\)

A) \(120\)

B) \(140\)

C) \(144\)

Answers

1. A) \(a^2−b^2=(a+b)(a−b)\)
2. B) \(x^2−16\)
3. B) \(−ab\) and \(ab\)
4. A) \(y^2−49\)
5. B) \(140\)

Practice

• More Examples

• Take the Quiz

Continue Learning

1. \((a – b)^2\) – Geometric Derivation
2. \((a + b)^2\) – Geometric Derivation
3. \(a^2 – b^2\) – Geometric Derivation
4. \(a^2 – b^2\) – Algebraic Proof

Navigation

• Back to Algebra
• Back to Home