Simplify 7x²(3x – 9) + 3 and find its values for x = 4 and x = 6

An algebraic expression, which is also known as a variable expression is an equation composed of variable terms formed from the combination of constants and variables. These components are joined together using operations, like addition, subtraction, multiplication, or division. The constants accompanied by the variable in each term are referred to as the coefficient. 

Solve the equation 7x²(3x – 9) + 3 for x = 4 and x = 6

Solution: 

⇒ 7x²(3x – 9) + 3

Find the solution for 7x²(3x – 9)

By using distributive law which states that; 

a(b – c) = ab – ac

So according to the law

⇒ (7x² × 3x)  – (7x² × 9) 

⇒ 21x³ – 63x²

Therefore,

⇒ 7x²(3x – 9) + 3 = 21x³ – 63x² + 3

Now we have to solve for the equation

21x³ – 63x² + 3

Further,

For x = 4,

⇒ 21x³ – 63x² + 3

⇒ 21 × 4³ – 63 × 4² + 3

⇒ 1344 – 1008 + 3

⇒ 336 + 3 

⇒ 339

Further,

Now for x = 6,

⇒ 21x³ – 63x²

⇒ 21 × 6³ – 63 × 6² + 3

⇒ 2268 + 3

⇒ 2271

Therefore,

The algebraic expression ⇒ 7x²(3x – 9) + 3

For the value of x = 4 is 339

For the value of x = 6 is 2271

Sample Questions

Question 1. By applying suitable algebraic identity, Find 1050²

Solution:

By applying the algebraic identity in the question: (a + b)² = a² + 2ab + b²

Thus, 

1050 = 1000 + 50

Therefore,

1050² = (1000 + 50)²

Here, 

a = 1000

b = 50

(1000 + 50)² = (1000)² + 2 × 1000 × 50 + (50)²

= 1000000 + 100000 + 2500

Therefore, 

1050² = 1102500.

Question 2. Simplify 82 + 2×(5x – 7). For the values of x = 2 and x = -2?

Solution:

Here we have,

82 + 2 × (5x – 7)

For x = 2

Substitute value of x = 2 in the equation

= 82 + 2 × (5x – 7)

= 82 + (2 × 5x  – 2 × 7)

= 82 + (10x – 14)

= 82 + 10x – 14

= 82 – 14 + 10 × 2

= 82 – 14 + 20

= 88

For x = -2

Substitute value of x = -2 in the equation

= 82 + 2 × (5x – 7)

= 82 + (2 × 5x  – 2 × 7)

= 82 + (10x – 14)

= 82 + 10x – 14

= 82 – 14 + 10 × (-2)

= 82 – 14 – 20

= 48

Question 3. Simplify 24 × 7  + x(365 – 65). For the value of x = 1 and x = -1

Solution:

Here we have

24 × 7 + x(365 – 65)

For x = 1

Substitute value of x = 1 in the equation

= 24 × 7 + x(365 – 65)

= 168 + x(365 – 65)

= 168 + 365x – 65x

= 168 + 300x

= 168 + 300 × 1

= 168 + 300

= 468

For x = -1

Substitute value of x = -1 in the equation

= 24 × 7 + x(365 – 65)

= 168 + x(365 – 65)

= 168 + 365x – 65x

= 168 + 300x

= 168 + 300 × (-1)

= 168 – 300

= -132

Question 4. Subtract the polynomials.

(6x + 3) from (-8x + 6)

And simplify for x = 4

Solution:

(6x + 3) from (-8x + 6)

= (-8x + 6) – (6x + 3)

= -8x + 6 – 6x – 3

= -8x -6x + 6 – 3

= -14x + 3

For x = 4

Substitute value of x = 4 in the equation

= -14 × 4 + 3

= -56 + 3

= -53

Question 5. Solve the equation 5x²(6x – 7) + 5 for x = 2 and x = 4

Solution:

5x²(6x – 7) + 5

Find the solution for

5x²(6x – 7)

By using distributive law which states that; 

a(b – c) = ab – ac

So according to the law

⇒ (5x² × 6x)  – (5x² × 7) 

⇒ 30x³ – 35x²

Therefore,

⇒ 5x²(6x – 7) + 5 = 30x³ – 35x² + 5

Now we have to solve for the equation

30x³ – 35x² + 5

Further,

For x = 4,

⇒ 30x³ – 35x² + 5

⇒ 30 × 4³ – 35 × 4² + 5

⇒ 1920 – 560 + 5

⇒ 1360 + 5 

⇒ 1365

Further,

Now for x = 6,

⇒ 30x³ – 35x² + 5

⇒ 30 × 6³ – 35 × 6² + 5

⇒ 6480 – 1260 + 5

⇒ 5220 + 5

⇒ 5225

Therefore,

The algebraic expression ⇒ 5x²(6x – 7) + 5

For the value of x = 4 is 1365

For the value of x = 6 is 5225