Simplify 7x2(3x – 9) + 3 and find its values for x = 4 and x = 6
Last Updated :
13 Oct, 2021
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
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