Simplification Example Problems

Simplification Example Problems:

Meaning of Simplification:


Simplification calculator is the online software in the Internet through which students in online give the question for simplification they get the answer to their questions. These simplification calculator is very much helpful for students to clear their doubts in their home work problems. Sample problems from algebra involves step by step simplification. The simplification calculator for algebra would be much useful for school students. let us see some sample problems from algebra for simplification calculator.

Example 1:


Find the sum of 2x4 – 3x2 + 5x + 3 and x + x3 – 6x2 – 1.

Solution:

Using the associative and distributive property, we obtain

(2x4 – 3x2 + 5x + 3) + (x3 – 6x2 + x – 1) = 2x4 + x3 – 3x2 – 6x2 + 5x + x + 3 – 1

= 2x4 + x3 – (3+6)x2 + (5+1)x + 2

= 2x4 + x3 – 9x2 + 6x + 2. (answer)

Example 2:

Factorize x2 – 8xy – x + 2y.

Solution:

x2 – 8xy – x + 2y = (x2 – 8xy) – (x – 2y)

= x(x – 8y) + (–1) (x – 2y)

= (x – 8y) [x + (–1)]

= (x – 8y) (x – 1). (answer).






Example 3:

Problem to find the variables x,y and z:

x + y + 2z = 8 ------> (1)

3x - y + 3z = 4 ------>(2)

2x + y + 4z = 6 ------>(3)

Solution:

Solve (1) and (2),

x + y + 2z = 8 ----> (1)

3x - y + 3z = 4 -----> (2)

add the above two equations.

we get 4x + 5z = 12 ------> (4)

solve (1) and (3)

(3) * 2 ----> 4x + 4y +8z = 16

(4) -----> 4x + 0y +5z = 12
(-) (-) (-)

3z = 4

[ z = 4/3]

substitute [z = 4/3] in (4) eqn

4x + 5 [(4/3)] = 12

4x = 12 - [20/3]

4x = [(36-20)/3] = [16 / 3]

x = [16/12] = [ 4/3]

substitute x = [4/3] , z = [4/3] in (1) eqn.

[4/3] + y + 2 [(4/3)] = 8

y + [12/3 ] = 8

y + 4= 8

y = 8 - 4 .

x = [4/3] , y = 4, z = [4/3] .

Example 4:

Find the sum of x3y + 2x2y2 – 3xy3 and 3x3 – 3x3y + y3 + 4xy3.

Solution:

(x3y + 2x2y2 – 3xy3) + (3x3 – 3x3y + y3 + 4xy3) = x3y + 2x2y2 – 3xy3 + 3x3 – 3x3y + y3 + 4xy3

= (x3y – 3x3y) + (2x2y2) + (–3xy3 + 4xy3) + (3x3) + (y3)

= –2x3y + 2x2y2 + xy3 + x3 + 3x3 + y3

Hope you like the above example of Simplification.Please leave your comments, if you have any doubts.