Quiz – a^2−b^2 – Algebraic Proof

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) \(144\)

Question 6

Expand:

\((2x+3)(2x-3)\)

A) \(4x^2-9\)

B) \(4x^2-12x+9\)

C) \(2x^2-9\)

Question 7

Which expression is equal to:

\(m^2-64\)

A) \((m+8)(m-8)\)

B) \((m+64)(m-64)\)

C) \((m-8)^2\)

Question 8

When expanding:

\((3a+b)(3a-b),\)

which two middle terms cancel?

A) \(-3ab\) and \(3ab\)

B) \(-ab\) and \(ab\)

C) \(-9ab\) and \(9ab\)

Question 9

Complete the factorisation:

\(x^2-81=(x+9)(\text{_____})\)

A) \(x+9\)

B) \(x-9\)

C) \(x-81\)

Question 10

Evaluate using the difference of two squares identity:

\(21^2-19^2\)

A) \(40\)

B) \(80\)

C) \(400\)

Answers

A) \(a^2−b^2=(a+b)(a−b)\)
B) \(x^2−16\)
B) \(−ab\) and \(ab\)
A) \(y^2−49\)
B) \(140\)
A) \(4x^2-9\)
A) \((m+8)(m-8)\)
A) \(-3ab\) and \(3ab\)
B) \(x-9\)
B) \(80\)

Mulkek