Simplify 5x(5x³ + 9²) + 4

In arithmetic, we deal with the number and different operations on the number. In geometry, we deal with the shape and angles of the structure. In the same way, in algebra, we deal with numerals, variables, and arithmetic operators. Numerals are terms that have a constant value and are represented by numbers. Variables are terms that do not have constant value and are represented by letters of alphabet or symbol.

By using symbols and letters, we can formalize the perimeter of a square. We know that a square has four sides and all the sides have the same dimension. Suppose the length of the side is ‘a’ unit. The perimeter of a square is the summation of all four sides. So,

Perimeter = a + a+ a+ a

                = 4a

Algebraic Expression 

An algebraic expression is the combination of numerals, variables, and operators. We can also represent a mathematical statement in mathematical terms. 

For example, Eight times a number taken away from 15 can be written as ’15 – 8x’. Here we represent unknowns by ‘x’ because we don’t know the value of the number.

In the expression, ’15 – 8x’, – sign separates the expression in two terms. The first term is 15 and another term is 8x. So on the basis of the number of terms an algebraic expression is categorized into the following types.

• Monomial: If the number of terms in an algebraic expression is one then the expression is known as the monomial. Example: 5x, 9y, etc.
• Binomial: If the number of terms in an algebraic expression is two then the expression is known as the binomial. Example: 5x+3y, 9-3r, etc.
• Trinomial: If the number of terms in an expression is three then the expression is known as trinomial. Example: 9x+9y-9z, a+b+c, etc.
• Polynomial: If the number of terms in an expression is one or more than one then the expression is known as the polynomial.

Simplify 5x(5x³ + 9²) + 4

Solution:

Step to solve the problem: 

Step 1: Solve the numerals part first, if the square sign is present on a number then write the square of the number.

= 5x (5x³ + 9²) + 4

=5x (5x³ + 81) +4

Step 2: Apply the distributive property of multiplication. For example: a×(b+c) = a×b + a×c

Here ‘a’ is distributed with b and c. 

= 5x (5x³ + 81) +4

= 5x × 5x³ + 5x × 81 + 4

Step 3: Multiply the numerals and variable part of the same term.

= 25x⁴ + 405x +4

So the simplification of 5x (5x³ + 9²) + 4 is 25x⁴+ 405x + 4.

Similar Questions

Question 1: Simplify: 6y(9y² +5³) – 4

Solution: 

In the given expression, first of all simplify the cube term.

= 6y(9y² + 5³) – 4

= 6y( 9y² + 5×5×5) – 4

= 6y(9y² +125) – 4

 Apply the distributive property of multiplication. For example: a×(b+c) = a×b + a×c

= 6y×9y² + 6y×125 -4

 Multiply the numerals and variable parts of the same term.

= 54y³ +750y -4

So the simplification of 6y(9y² +5³) -4 is  54y³ +750y -4.

Question 2: Simplify: 3x(x³ – 5²) + 9

Solution:

Simplify the square term on numerals.

= 3x (x³ – 5×5) +9

= 3x (x³ -25) +9

 Apply the distributive property of multiplication. For example: a×(b+c) = a×b + a×c

= 3x×x³ – 3x×25 +9

 Multiply the numerals and variable parts of the same term.

= 3x⁴ – 75x +9

So the simplification of 3x(x³ – 5²) + 9 is 3x⁴ – 75x +9.