Concept of Find the Error:
There are many errors students commonly make when solving algebra exercises. You should avoid making such errors.
- Coefficient 1 of a term is usually not shown. But while adding like terms, we include it in the sum.
x + 2x + 3x = 5x
The correct statement is x + 2x + 3x = 6x.
- Coefficient 1 of a term is usually not shown. But while subtracting like terms, we include it in the subtraction.
5y + 2y + y − 7y = 0.
The correct statement is 5y + 2y + y − 7y = y.
- When you multiply the expression enclosed in a bracket by a constant (or a variable) outside, each term of the expression has to be multiplied by the constant (or the variable).
4(x − 5) = 4x − 5
The correct statement is 4(x − 5) = 4x − 20.
- When you square a monomial, the numerical coefficient and each factor has to be squared.
(2x)2 = 4x
The correct statement is (2x)2 = 4x2.
- Make sure, before applying any formula, whether the formula is really applicable.
(x – 5)2 = x2 – 25
The correct statement is (x – 5)2 = x2 – 10x + 25.
- While dividing a polynomial by a monomial, we divide each term of the polynomial in the numerator by the monomial in the denominator.
`(3x^2 + 1)/(3x^2)` = 1 + 1 = 2
The correct statement is `(3x^2 + 1)/(3x^2) = 1 + 1/(3x^2)`.
Find and correct the errors in the following mathematical statement. Substituting x = −3 in x2 + 5x gives (−3)2 + 5 (−3) = −9 − 15 = −24
Find and correct the errors in the following mathematical statement. Substituting x = −3 in
x2 + 5x + 4 gives (−3)2 + 5 (−3) + 4 = 9 + 2 + 4 = 15