Question 13 of 27beginner🔍 AnalyzeTrue / False2 marks

(−q+2)2=q2−4q+4(-q + 2)^2 = q^2 - 4q + 4

Correct Answer

True. The expansion is correct. Using Identity 1A with a=−qa = -q and b=2b = 2: (−q+2)2=(−q)2+2(−q)(2)+22=q2−4q+4(-q + 2)^2 = (-q)^2 + 2(-q)(2) + 2^2 = q^2 - 4q + 4.

Exercise: Mind the Mistake, Mend the Mistake | Q: 5 | (Page Page 15)
For More Understanding

Explanation

The chapter shows that (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 works even when aa is negative. Here, (−q)2=q2(-q)^2 = q^2 since squaring a negative gives a positive, and 2(−q)(2)=−4q2(-q)(2) = -4q.

Solution Steps

  1. Apply Identity 1A: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2

  2. With a=−qa = -q and b=2b = 2:

  3. (−q+2)2=(−q)2+2(−q)(2)+22(-q + 2)^2 = (-q)^2 + 2(-q)(2) + 2^2

  4. =q2−4q+4= q^2 - 4q + 4

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