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Algebra Solver Free

Algebra is one subject where you can never have enough practice. The more you work out problems, the easier they become. You won’t find much time or opportunity to practice in the classroom, where the focus is on teaching new methods and covering the topics in the curriculum. You will have to make time to work out problems. But how do you know if your work is correct? This is where free algebra problem solvers come in. Free online algebra solvers provide students with practice problems and worksheets and also check your work and correct any mistakes. Most of the free online algebra solvers or algebra free solvers have plenty of practice material and also explain any bits that you don’t know. The explanations are simple and straight forward and are easily understood by students of all grades.

Algebra Solver Free Online 

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With a free math solver algebra becomes much simpler. It is already immensely popular with students for algebra 1 and algebra 2. Free college algebra solvers cover advanced topics taught in college level. Students find the step by step solutions, that free online algebra solvers provide, especially helpful. Free online algebra solvers are comprehensive in their coverage of high school and college level algebra. Free algebra problem solvers are a great aid in enriching your learning experience. Some sites have sophisticated algebra solvers which can analyze equations in all their forms. The free algebra solvers have made studying algebra much easier with their simple approach, detailed examples and 24 X 7 availability.

Solved Examples

Question 1: Solve (3x - y)2 - 12(x + 4y) + 23
Solution:
Given (3x - y)2 - 12(x + 4y) + 23

Here polynomial is divided into three parts so it is a trinomial.

Step 1:

Solve each part of the polynomial

First part
(3x - y)2 = (3x)2 + y2 - 2 * 3x * y

= 9x2 + y2 - 6xy

[(a - b)2 = a2 + b2 - 2ab]

Second part

12(x + 4y) = 12 * x + 12 * 4y

= 12x + 48y

Third part


23 = 23

Step 2:

=> (3x - y)2 - 12(x + 4y) + 23 = 9x2 + y2 - 6xy - (12x + 48y) + 23

= 9x2 + y2 - 6xy - 12x - 48y + 23

=> (3x - y)2 - 12(x + 4y) + 23 = 9x2 + y2 - 6xy - 12x - 48y + 23. answer
 

Question 2: Solve a - 16a-3
Solution:
Given a - 16a-3
Here common factor is 'a'.

Step 1:

When factoring the common factor, take the lowest power of the factor.

Lowest power of the factor = a-3

=> a - 16a-3  =  a-3 ($\frac{a}{a^{-3}}$ - 16)

= a-3 ($\frac{a^1}{a^{-3}}$ - 16)

= a-3 ($a^{1 - (-3)}$ - 16)

[$\frac{a^m}{a^n}$ = $a^{m - n}$]

= a-3 ($a^{1 + 3}$ - 16)

=  a-3 (a- 16)

Step 2:
To eliminate the negative exponent, convert it into a fraction.

=> a-3 (a- 16) = $\frac{1}{a^{3}}$ (a4 - 16)

= $\frac{1}{a^{3}}$ (a4 - 24)

= $\frac{1}{a^{3}}$ ($(a^2)^2 - (2^2)^2$)

[a2 - b2 = (a - b)(a + b)]

= $\frac{1}{a^{3}}$(a2 - b2 )(a2 + b2 )

= $\frac{1}{a^{3}}$(a - b)(a + b)(a2 + b2 )

=> a-3 (a- 16) = $\frac{1}{a^{3}}$(a - b)(a + b)(a2 + b2 )
 

Question 3: What is the point of intersection of the lines: x + 2y = 3 and x + y = 7

Solution:
Given equation of lines are x + 2y = 3 and x + y = 7

Step 1:
Since the point of intersection lie on the two lines, its coordinates x and y satisfy the two equations simultaneously.
To find the point of intersection, find the values of x and y

x + 2y = 3                          ................................(1)

x + y = 7                           ..................................(2)

Step 2:
Eliminate y from equation (1), choose equation (2)

=> y = 7 - x                     .....................................(3)

(3) put in (1)

=> x + 2(7 - x) = 3

=> x + 14 - 2x = 3

=> - x + 14 = 3

=> - x = 3 - 14

=> - x = - 11

=> x = 11

Step 3:
To find the value of y put x = 11 in equation (3).  

=> y = 7 - 11

=> y = - 4

Hence the point of intersection of the lines is (x, y) = (11, - 4). answer