Which identity can quickly find ( 45\times55 )?
Answer and explanation
Correct answer: ( (a+b)(a-b)=a^2-b^2 )
The numbers 45 and 55 are equally distant from 50: they can be written as \\(50-5\\) and \\(50+5\\). Their product therefore has the form \\((a-b)(a+b)\\), which uses the identity \\((a+b)(a-b)=a^2-b^2\\). Taking \\(a=50\\) and \\(b=5\\), we get \\(45\\times55=(50-5)(50+5)=50^2-5^2\\). The identity named in option C is exactly this rule.
Thus option C is correct. If the value is required, it is \\(2500-25=2475\\). Options A and B are square identities but do not directly represent the product of two conjugate binomials. Option D is an identity for three terms and is unnecessary here. The useful pattern is two numbers equally placed around a common centre.
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What is the correct answer to this question?
( (a+b)(a-b)=a^2-b^2 )
Why is this the correct answer?
The numbers 45 and 55 are equally distant from 50: they can be written as \\(50-5\\) and \\(50+5\\). Their product therefore has the form \\((a-b)(a+b)\\), which uses the identity \\((a+b)(a-b)=a^2-b^2\\). Taking \\(a=50\\) and \\(b=5\\), we get \\(45\\times55=(50-5)(50+5)=50^2-5^2\\). The identity named in option C is exactly this rule.
Thus option C is correct. If the value is required, it is \\(2500-25=2475\\). Options A and B are square identities but do not directly represent the product of two conjugate binomials. Option D is an identity for three terms and is unnecessary here. The useful pattern is two numbers equally placed around a common centre.
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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