Largest Expressions in Math

Introduction to Largest Expressions in Math:

In math expressions is of the form ax + b, where a and b is known as constants and x is variable. Determination of value depends upon the variables occurring in the expression. Instead of writing in words, expression is in form of variables, constants, symbols, relation, and operations. The expression with more than two or more variables is called as largest expressions in math.  Let us see about largest expressions in math in this article.

Worked Examples to Largest Expressions in Math

Example 1:

Solve the largest expression ax+ ay + bx + by + cx + cz + dx + dz + dy by factorizing.

Solution:

Step 1:

Let us write the given expression as ax + ay + bx + by + cx + cz + dx + dy + dz.
Step 2:

Factorize the a term alone, we get,

ax + ay = a(x + y)

Step 3:

Factorize the b term alone we get,

bx + by = b(x + y)

Step 4:

Factorize the c term alone, we get,

cx + cz = c(x + z)

Step 5:

Factorize the d term alone, we get,

dx + dy + dz = d(x + y + z)

Step 6:

Combine the step (2), (3), (4) and (5), we get,

ax + y) + b(x + z) c(x + z) + d(x + y + z)

Therefore, the solution for solving the largest expression is ax + y) + b(x + z) c(x + z) + d(x + y + z).

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Another Problem to Largest Expressions in Math

Example 2:

Solve the largest expression ax + 2ay^2 – bx – 2by^2 + 2ax – 6ay – bx + 3by.

Solution:

Step 1:

Let us write the given largest expression is ax + 2ay^2 – bx – 2by^2 + 2ax – 6ay – bx + 3by.

Step 2:

Take the common term a from the first and second terms, we get,

ax + 2ay^2 = a(x + 2y^2)

Step 3:

Take the common term b from the third and fourth term, we get,

-bx – 2y^2 = -b(x + 2y^2)

Step 4:

From step (2) and (3), combine the term, we get,

ax + 2ay^2 – bx – 2by^2  = (a – b) (x + 2y^2)

Step 5:

Take the common term 2a form the fifth and sixth term, we get,

2ax – 6ay = 2a(x – 3y)

Step 6:

Take the common term –b from the seventh and eighth term, we get,

-bx + 3by = - b (x – 3y)

Step 7:

From step (5) and (6), combine the term, we get,

2ax – 6ay – bx + 3by = (2a – b) (x – 3y)

Step 8:

Combine step (4) and (7) of the largest expression of the given problem,

ax + 2ay^2 – bx – 2by^2 + 2ax – 6ay – bx + 3by = (a – b) (x + 2y^2) + (2a – b) (x – 3y)

Therefore, the solution for solving the largest expression is (a – b) (x + 2y^2) + (2a – b) (x – 3y).