简化 7x2(3x – 9) + 3 并找到 x = 4 和 x = 6 的值

化简 7x ² (3x – 9) + 3 并找到 x = 4 和 x = 6 的值

代数表达式，也称为变量表达式，是由常数和变量组合形成的变量项组成的方程。这些组件使用运算连接在一起，例如加法、减法、乘法或除法。每一项中伴随变量的常数称为系数。

对于 x = 4 和 x = 6，求解方程 7x ² (3x – 9) + 3

解决方案：

⇒ 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

示例问题

问题 1. 通过应用合适的代数恒等式，找到 1050 ²

解决方案：

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.

问题 2. 简化 82 + 2×(5x – 7)。对于 x = 2 和 x = -2 的值？

解决方案：

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

问题 3. 简化 24 × 7 + x(365 – 65)。对于 x = 1 和 x = -1 的值

解决方案：

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

问题 4. 减去多项式。

(6x + 3) 从 (-8x + 6)

并简化为 x = 4

解决方案：

(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

问题 5. 求解方程 5x ² (6x – 7) + 5 对于 x = 2 和 x = 4

解决方案：

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