Question

Find and correct the errors in the statement: (2x)^2 + 4(2x) + 7 = 2x^2 + 8x + 7

Answer 1

Given :  (2x)² + 4(2x) + 7 = 2x² + 8x + 7

 

Concept :  

Common errors we done by solving algebraical expression and equation:

Error 1

Coefficient 1 of a term is usually not written. So we often ignore that. But while adding like terms, we should include it in the sum.

Error 2

When we multiply the expression enclosed in a bracket by a constant (or a variable) outside, we usually applied the multiplication to the first term only. This is the wrong calculation. Each term of the expression has to be multiplied by the constant (or the variable).

Error 3

when we square a monomial, we usually ignored the numerical coefficient. This is the wrong method. The numerical coefficient and each factor has to be squared.

Error 4

when we square a binomial, we usually do not apply the proper identity. This is the wrong approach. The right identity should be used.

Error 5

While dividing a polynomial by a monomial, We usually don’t divide each term of the polynomial in the numerator by the monomial in the denominator.

 

Solution:

We have : (2x)² + 4(2x) + 7 = 2x² + 8x + 7

LHS = (2x)² + 4(2x) + 7

= 4x² + 8x + 7

 

RHS = 2x² + 8x + 7

LHS ≠ RHS

 

Correct statement  :

(2x)² + 4(2x) + 7 = 4x² + 8x + 7

Hope this answer will help you….

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Answer 2

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L.H.S = (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7 ≠ R.H.S The correct statement is (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7