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Some Important Facts of Algebra:

A mathematical statement on behalf of the equality of two terms is known as an equation. There will be always an equal to sign in between the expressions.

An algebraic equation of degree one is known as linear equation. An equation of degree two is known as quadratic equation.  Examples: $x + 5$ = $9$ is a linear equation while $x^2 + 4x + 4$ = $0$ is a quadratic equation.

The value of $x$ for which the equation gets satisfied is known as the solution to the equations.

In algebra, we can explain if we change the order that will not change their sum. 

For Example: $(x + y) + z$ = $x + (y + z)$.

• If we add zero to any number the answer will be the number itself. For example $x + 0$ = $x$

• If two sides of an equation are equal we can add or subtract the same number to both sides.   

For Example: If $x$ = $y$ the $x + z$ = $y + z$ and $x - z$ = $y - z$.

Order of operations to be explain: Operations inside the parenthesis or bracket of algebra equations are done first. Next we do operations involving exponents. Multiplication and division from left to right are done next.  The addition and subtraction from left to right are done as a final operation. In short PEMDAS.

•  Multiplication is written in three different ways. For example $5$ multiplied by $x$ can be written as $5 \times x$ or $5x$ or $5(x)$.

Bar in fraction is division  symbol. For example $\frac{x}{y}$ means $x$ divided by $y$.

Changing the order of the multiplying numbers will not change the value. For example $xy$ = $yx$.

• Zero times a number is zero and one time any number is the number itself.

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Important Topics in Algebra

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1) Polynomials

2) Algebraic Identities

3) Factorization

4) Permutations & Combinations

5) Ratio

6) Quadratic Equation.


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Example 1: 

Solve $2x + 3x$


$2x + 3x$ = $(2 + 3)\ x$

= $5x$
Example 2:

Multiply $3ab$ and $4b$


$(3 ab) \times (4b)$ = $(3ab) \times (4b)$

= $3ab^2 \times 4$

= $3 \times (4ab^2)$

= $12 \times ab^2$

= $12ab^2$

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