#### notes

**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}= 4x^{2}. - Make sure, before applying any formula, whether the formula is really applicable.

(x – 5)^{2}= x^{2}– 25

The correct statement is (x – 5)^{2}= x^{2}– 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)`.

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