What is the expansion of \((4x-5)^2\)?
Answer and explanation
Correct answer: 16x^2-40x+25
Apply the identity \((a-b)^2=a^2-2ab+b^2\). Here, \(a=4x\) and \(b=5\). Thus, \((4x-5)^2=(4x)^2-2(4x)(5)+5^2=16x^2-40x+25\). Option B incorrectly calculates the middle term as \(-20x\). Exam tip: in the square of a binomial, the middle term is twice the product of the two terms, with the appropriate sign.
Frequently asked questions
What is the correct answer to this question?
16x^2-40x+25
Why is this the correct answer?
Apply the identity \((a-b)^2=a^2-2ab+b^2\). Here, \(a=4x\) and \(b=5\). Thus, \((4x-5)^2=(4x)^2-2(4x)(5)+5^2=16x^2-40x+25\). Option B incorrectly calculates the middle term as \(-20x\). Exam tip: in the square of a binomial, the middle term is twice the product of the two terms, with the appropriate sign.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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