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In this lesson, we will learn how to identify and factor quadratics that are perfect trinomials and how to complete the factorization.

Q1:

For which values of π is 1 6 π₯ + π π₯ + 8 1 2 a perfect square?

Q2:

Complete the expression 1 6 π₯ + π¦ 4 2 to make a perfect square.

Q3:

Which of the following is a perfect square?

Q4:

Complete the quadratic expression 9 π₯ + 1 4 4 2 to make a perfect square.

Q5:

If 9 π¦ + 3 0 π¦ + π 2 is a perfect square, what is the value of π ?

Q6:

Complete the expression β 6 0 π₯ + 2 5 2 to make a perfect square.

Q7:

Complete the expression 4 2 5 π + 1 9 π 2 2 to make a perfect square.

Q8:

If π π¦ β 2 4 π¦ + 9 2 is a perfect square, what is the value of π ?

Q9:

Factorise fully 9 π₯ + 3 6 π₯ π¦ + 3 6 π¦ 4 2 2 4 .

Q10:

Factorise fully π₯ β 1 0 π₯ π¦ + 2 5 π¦ 2 2 .

Q11:

By factorising or otherwise, evaluate ( 1 0 . 1 ) β 4 . 2 Γ 1 0 . 1 + ( 2 . 1 ) 2 2 .

Q12:

Factorise fully 8 1 π + 1 8 π + 1 2 .

Q13:

Factorise fully 4 ( π₯ β 7 ) β 1 6 ( π₯ β 7 ) ( π¦ β 6 ) + 1 6 ( π¦ β 6 ) 2 2 .

Q14:

Complete the expression 8 1 π₯ + 9 0 π₯ π¦ + β― 2 to make a perfect square.

Q15:

Factorise fully 4 9 8 1 π₯ + 8 9 π₯ + 1 6 4 9 2 .

Q16:

Expand and simplify 5 π₯ ( 5 π₯ + 1 8 π¦ ) + 8 1 π¦ ο¨ , then factorise the result.

Q17:

By factorising or otherwise, evaluate ( 9 7 ) + 6 Γ 9 7 + 9 ο¨ .

Q18:

Factorise fully 0 . 1 6 π + 7 . 2 π + 8 1 2 .

Q19:

Factorise fully 1 3 6 π₯ β π₯ + 9 2 .

Q20:

Given that π₯ + 2 π₯ π¦ + π¦ = 8 1 2 2 , what are the possible values of π₯ + π¦ ?

Q21:

Factorise fully π + 6 π + 9 π οͺ ο .

Q22:

Factorise fully 6 4 π¦ π₯ β 6 4 π¦ π₯ + 1 6 π¦ 2 .

Q23:

Write all possible expressions for π such that π₯ + π + 4 π¦ 2 2 is a perfect square.

Q24:

Factorise fully ( π + 4 π ) + 1 4 π ( π + 4 π ) + 4 9 π 2 2 4 .

Q25:

Expand and simplify ( 3 π₯ + π¦ ) β 1 2 π₯ π¦ 2 , and then factorise the result completely.

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