# Basic Algebra

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### Learn More About Basic Algebra

CalculatorCrave basic algebra calculator can solve algebraic expressions, simplify them, factorize them, and expand simple to complex expressions quicker.

How to use the expression calculator

##### Simplifying algebraic expression

##### Write \frac{(x^2y)}{(xy^2 - xy)} as (x^2*y) / (x*y^2 - x*y)

##### Expanding algebraic expression

##### Write (3x +4y)(x − y) as / (3x +4y)(x − y)

##### 1. Using brackets with basic operations in algebra:

When dealing with algebraic expressions, it is important to use brackets to ensure the correct order of operations is followed. Brackets help in clarifying which operations should be performed first and can prevent errors in calculations.

For example, consider the expression 3 + 2 \times 4. Without brackets, it may be unclear whether to perform the addition first or the multiplication first.

However, by writing it as 3 + (2 \times 4) , it is clear that the **multiplication should be done** before the **addition**.

##### 2. Understanding factorisation

Factorisation is the process of expressing an algebraic expression as a product of its factors. This is done by finding common factors in the expression and factoring them out.

For example, consider the expression 6x + 9 . By identifying that both terms have a common factor of 3, the expression can be factorised as 3(2x + 3) .

##### 3. Factorising simple algebraic expressions

To factorise a simple algebraic expression, one must look for the highest common factor in all the terms and then factor it out.

For example, consider the expression 2x^2 + 4x . The highest common factor in this expression is 2x, so the expression can be factorised as 2x(x + 2).

Another example is the expression 4y^2 - 9 , which can be factorised as (2y + 3)(2y - 3) by applying the difference of squares formula.

##### Practice questions and answers

1. Simplify the expression 3(4+2).

Answer: 18

2. Factorise the expression x^2 + 4x + 4.

Answer: (x+2)^2

3. Expand the expression 2(3x-5).

Answer: 6x-10

4. Factorise the expression x^2 - 9.

Answer: (x+3)(x-3)

5. Simplify the expression 4(2x-1) - 3(3x+2).

Answer: 5x-11

6. Factorise the expression 9x^2 - 25.

Answer: (3x-5)(3x+5)

7. Expand the expression 2(3x+5).

Answer: 6x+10

8. Factorise the expression x^2 - 16.

Answer: (x+4)(x-4)

9. Simplify the expression 7(2x+3) - 4(3x-1).

Answer: -4x+19

10. Factorise the expression 4x^2 - 25.

Answer: (2x+5)(2x-5)

11. Expand the expression 3(2x+4).

Answer: 6x+12

12. Factorise the expression x^2 - 36.

Answer: (x+6)(x-6)

13. Simplify the expression 5(3x-2) - 2(2x+1).

Answer: 13x-12

14. Factorise the expression x^2 - 49.

Answer: (x+7)(x-7)

15. Expand the expression 4(3x+2).

Answer: 12x+8