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In this lesson, we will learn how to determine when a quadratic is a difference of two squares and then use this property to factor the expression.

Q1:

Completely factor .

Q2:

Q3:

Q4:

Q5:

Q6:

Q7:

Q8:

Q9:

If 𝑥 𝑦 = 8 , what is the value of ( 𝑥 + 3 𝑦 ) − ( 𝑥 − 3 𝑦 ) 2 2 ?

Q10:

If 𝑥 − 8 1 𝑦 = 2 4 2 2 and 𝑥 + 9 𝑦 = 6 , what is the value of 5 𝑥 − 4 5 𝑦 ?

Q11:

If 𝑥 − 1 6 𝑦 = − 8 0 2 2 and 𝑥 + 4 𝑦 = 5 , what is the value of 4 𝑦 − 𝑥 ?

Q12:

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Q15:

By factoring or otherwise, evaluate .

Q16:

If 𝑎 + 3 𝑏 = − 9 ( 𝑎 − 3 𝑏 ) = 2 7 , what is the value of 𝑎 − 9 𝑏 2 2 ?

Q17:

Q18:

By considering the difference of two squares, evaluate 9 1 × 8 9 without a calculator.

Q19:

If 𝑥 > 1 0 𝑦 , 𝑥 − 2 0 𝑥 𝑦 + 1 0 0 𝑦 = 3 6 2 2 , and 𝑥 + 1 0 𝑦 = 2 , what is the value of 𝑥 − 1 0 0 𝑦 2 2 ?

Q20:

Q21:

If 2 5 𝑥 − 1 6 𝑦 = 5 𝑥 + 4 𝑦 2 2 , what is the value of 5 𝑥 − 4 𝑦 ?

Q22:

By considering the difference of two squares, find the value of 𝑥 for which 3 9 − 1 9 = 2 0 𝑥 2 2 .

Q23:

Q24:

Q25:

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