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Factorization of Trinomial Perfect Square
Fill in the gap to make each of the following expression as a perfect square
[Factorization of Trinomial Perfect Square]
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Total Questions:
23
PART A: Positive Middle Term Expressions ($a^2 + 2ab + b^2$)
1.a
Fill in the gap to make $a^2 + \dots + 16$ a perfect square.
Solution:
The given expression is:
$$a^2 + \dots + 16$$
Writing first and last terms inside brackets as squares:
$$(a)^2 + \dots + (4)^2$$
So, the missing term $= 2 \times a \times 4$
$$= 8a$$
Hence, $8a$ is required to make the given expression a perfect square.
1.b
Fill in the gap to make $m^2 + \dots + 16$ a perfect square.
Solution:
Given expression:
$$m^2 + \dots + 16$$
Expressing terms in brackets:
$$(m)^2 + \dots + (4)^2$$
So, the missing term $= 2 \times m \times 4$
$$= 8m$$
Hence, $8m$ is required to make the given expression a perfect square.
1.c
$$4x^2 + \dots + 16$$
1.d
$$a^2b^2 + \dots + c^2d^2$$
1.e
$$9y^2 + \dots + 36$$
1.f
$$4m^2 + \dots + \frac{1}{9}$$
PART B: Negative Middle Term Expressions ($a^2 – 2ab + b^2$)
2.a
Fill in the gap to make $x^2 – \dots + 4$ a perfect square.
Solution:
Given expression:
$$x^2 – \dots + 4$$
Writing in brackets as perfect squares:
$$(x)^2 – \dots + (2)^2$$
Therefore, required middle term $= 2 \times x \times 2$
$$= 4x$$
Hence, $4x$ is required to make the given expression a perfect square.
2.b
Fill in the gap to make $m^2 – \dots + 121$ a perfect square.
Solution:
Given expression:
$$m^2 – \dots + 121$$
Writing in brackets as perfect squares:
$$(m)^2 – \dots + (11)^2$$
Therefore, required middle term $= 2 \times m \times 11$
$$= 22m$$
Hence, $22m$ is required to make the given expression a perfect square.
2.c
$$x^2 – \dots + 16$$
2.d
$$16y^2 – \dots + 1$$
2.e
$$9x^2 – \dots + 36$$
📖 CDC Textbook Factorization Questions & Solutions
Selected exercise problems from Curriculum Development Centre textbook
Note for Students:
Some key and important questions from CDC Question No. 1 have been solved here. You can solve the remaining questions using the same steps. If you encounter any issues during your practice, feel free to contact us via the form below!
Question 1: Factorize the following expressions into Perfect Squares
1.a
$$a^2 + 12a + 36$$
1.b
$$y^2 + 14y + 49$$
1.i
$$p^2 – 26p + 169$$
1.e
$$9r^2 + 60r + 100$$
1.f
$$36x^2 + 84x + 49$$
1.l
$$49r^2 – 70r + 25$$
1.o
$$\frac{x^2}{16} – xy + 4y^2$$
1.r
$$25x^2 – 2xy + \frac{y^2}{25}$$
Question 2: Some Harder Problems (Using $A^2 – B^2$ Combination)
2.a
$$a^2 + 12a + 36 – b^2$$
2.b
$$y^2 + 16y + 64 – z^2$$
2.c
$$p^2 + 26p + 169 – 9q^2$$
2.d
$$4a^2 – b^2 + 20b – 100$$
2.e
$$9r^2 – s^2 – 6s – 9$$
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