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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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