What is the main difference between ( (2x+3)(2x-3) ) and ( (2x-3)^2 )?
Answer and explanation
Correct answer: The first is a difference of squares, whereas the second gives a perfect-square trinomial
The first expression contains conjugate binomials:
(a+b)(a-b)
. Hence, using
(a+b)(a-b)=a^2-b^2
,
(2x+3)(2x-3)=4x^2-9
; there is no middle x-term. The second expands as
(2x-3)^2=4x^2-12x+9
, which is a perfect-square trinomial and has the middle term
-12x
. Therefore, option A is correct; option C reverses the two identities. Exam tip: recognise
(a+b)(a-b)
as a difference of squares and
(a-b)^2
as a perfect square.
Frequently asked questions
What is the correct answer to this question?
The first is a difference of squares, whereas the second gives a perfect-square trinomial
Why is this the correct answer?
The first expression contains conjugate binomials:
(a+b)(a-b)
. Hence, using
(a+b)(a-b)=a^2-b^2
,
(2x+3)(2x-3)=4x^2-9
; there is no middle x-term. The second expands as
(2x-3)^2=4x^2-12x+9
, which is a perfect-square trinomial and has the middle term
-12x
. Therefore, option A is correct; option C reverses the two identities. Exam tip: recognise
(a+b)(a-b)
as a difference of squares and
(a-b)^2
as a perfect square.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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