Question

Simplify: (a²+ b²+ c²)(a³) + (a³–b³–c³) (b³)

Verify your result in the above problem for a =1, b =1, c= 2​

Answer 1

Given

a = 1

b = 1

c = 2

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To Find

The value of expression with the values of variables.

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Solution

First of all we have two methods to solve this.

Method 1

Simplify the expression and then substitute the values of the variables, 'a', 'b' and 'c'.

Step 1: Distribute the variables.

⇒ (a²+ b²+ c²)(a³) + (a³-b³-c³) (b³)

⇒ (a³)(a²) + (a³)(b²) + (a³)(c²) + (b³)(a³) + (b³)(-b³) + (b³)(-c³)

⇒ a³⁺² + a³b² + a³c² + a³b³ - b³⁺³ - b³c³

⇒ a⁵ + a³b² + a³c² + a³b³ - b⁶ - b³c³

Step 2: Give the value of the variables and solve.

⇒ (a²+ b²+ c²)(a³) + (a³-b³-c³) (b³)

⇒ 1⁵ + 1³×1² + 1³×2² + 1³×1³ - 1⁶ - 1³×2³

⇒ 1 + 1 + 4 + 1  - 1 - 8

⇒ 7 - 1 - 8

⇒ 6 - 8

⇒ -2

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Method 2

We'll just give value of 'a' 'b' and 'c' and solve.

Step 1: Give the value to the variables.

⇒  (a²+ b²+ c²)(a³) + (a³-b³-c³) (b³)

⇒  (1²+ 1²+ 2²)(1³) + (1³-1³-2³) (1³)

⇒ (1 + 1 + 4)(1) + (1 - 1 - 8)(1)

⇒ (2 + 4)(1) + -8(1)

⇒ 6(1) + -8(1)

⇒ 6 + - 8

⇒ 6 - 8

⇒ -2

∴ With the given values of the variables in the equation we get the answer as (-2)

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