Solve (4a2 – 2a +15) + (a2 + 3a – 11)

Algebra is the branch of mathematics that deals with the study of numerals and variables. It helps to represent the conditions or problems in the mathematical expressions. Most of the branches of mathematics like calculus, coordinate geometry, etc use algebra. It uses variables like p, q, r, s, and operations like division, subtraction, multiplication, and addition to create an expression. For example, 4x + 2y = 10. Here, a and y are the variables, and + represents the addition operation.

Algebraic Expression

An algebraic expression is composed of various parts, constants, variables, and mathematical operations. It can be combined together using various mathematical operations, such as addition(+), subtraction(-), multiplication(x), and division(/). It is also known as a mathematical statement.

Addition of algebraic expression

When adding the algebraic expressions we have to gather all the like terms and add them together. Or we can say that the sum of the many like terms will be the like term whose coefficient is the total of the coefficients of the like terms.

Steps to solve algebraic expression

Step 1: The brackets are opened along with the evaluation of signs.

Step 2: The terms that contain the same power of the variable are collected together.

Step 3: The like terms are solved to achieve a singular term for each of the variables.

Step 4: The simplified result is obtained as the final answer.

Solve (4a² – 2a +15) + (a² + 3a – 11)

Solution: 

We have, 

(4a² – 2a + 15) + (a² – 3a – 11)

Open the brackets

4a² – 2a + 15 + a² – 3a – 11

Take all the like terms together as follows

4a² + a² – 2a – 3a + 15 – 11

Now calculating the values,

5a² + 5a + 4 

Therefore, this equation can be simplified to obtain the following answer. 

Sample Questions

Question 1. Simplify 6(4x – 2) + x((3x)/ (3)) + 16 – 5x

Solution:

Here we have 6(4x – 2) + x((3x)/ (3)) + 16 – 5x

First open brackets

⇒ 24x – 12 + 3x²/3 + 16 – 5x

simplifying

⇒ 24x – 12 + x² + 16 – 5x

Now taking the like terms together

⇒ x² + 24x – 5x – 12 + 16 

Now simplify the like terms

⇒ x² + 19x + 4 

Question 2. Simplify 2x (8 – 2x) – 2x (6 – 2x)

Solution:

Here we have to simplify 2x (8 – 2x) – 2x (6 – 2x)

First open the brackets

⇒ 16x – 4x² – 12x + 4x²

Now combine the like terms

⇒ -4x² + 4x² + 16x – 12x

Further simplifying the like terms

⇒ 4x

Question 3. Simplify 4st + 6t – 2s + 10t + 8s

Solution:

Here we have to simplify 4st + 6t – 2s + 10t + 8s

Take the like terms together

⇒ 4st + 6t + 10t – 2s + 8s

Now do the addition and subtraction of the like terms

⇒ 4st + 16t + 6s

Therefore,

Simplification of 4st + 6t – 2s + 10t + 8s is 4st + 16t + 6s

Question 4. Simplify x(2x + 3y – 4) – x ² + 4xy – 12x?

Solution:

Here we have to simplify  x(2x + 3y – 4) – x ² + 4xy – 12x

First open the brackets

⇒ 2x² + 3xy – 4x – x² + 4xy – 12x

Now take all the like terms together

⇒ 2x² – x² + 3xy + 4xy – 4x – 12x

Now solving the like terms

⇒ x² + 7xy – 16x