Find and correct the errors in the statement: (3x + 2)^2 = 3x^2 + 6x + 4
Answers
Answer:
(a+b)^2=a^2+b^2+2ab
(3x+2)^2= (3x)^2+2^2+2*3x*2
= 9x^2+4+12x. (correct equation)
Given : (3x + 2)² = 3x² + 6x + 4
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 : (3x + 2)² = 3x² + 6x + 4
LHS = (3x + 2)² = 9x² + 12x + 4
[(a + b)² = a² + b² + 2ab]
RHS = 3x² + 6x + 4
LHS ≠ RHS
Correct statement :
(3x + 2)² = 9x² + 12x + 4
Hope this answer will help you….
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