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Concept of Find the Error

notes

Concept of Find the Error:

There are many errors students commonly make when solving algebra exercises. You should avoid making such errors.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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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