Question

Find the value using relevant algebraic expression. a.) 1003 × 998. b.) (a^2+b^2)(-a^2+b^2) . Question is correct. Please show steps and I'll mark brainliest. Thank you ​

Answer 1

Answer:

1. 1003 × 998 = 100994
2. (a² + b²) (-a² + b²) = b⁴ - a⁴

Step-by-step explanation:

First part:

(1003 × 998)

This can also be written as:

(1000 + 3) × (1000 - 2)

Now, this is of the form:

(x + a) (x + b) = x² + x(a + b) + ab

where:

• x = 1000
• a = 3
• b = -2

So the value of the expression becomes,

(1000)² + 1000 (3 - 2) + 3(-2)

= 10000000 + 1000 - 6

= 100994

∴ 1003 × 998 = 100994

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Second part:

(a² + b²) (-a² + b²)

On rearranging we can also write this as:

(b² + a²) (b² - a²)

Now, this is of the form:

(x + y) (x - y) = x² - y²

where:

• x = b²
• y = a²

Applying the above identity,

(b² + a²) (b² - a²)

= (b²)² - (a²)²

= b⁴ - a⁴

∴ (a² + b²) (-a² + b²) = b⁴ - a⁴

Answer 2

Step-by-step explanation:

(1003)^2 can be written as (1000+3)^2

so it evaluates to (1000)^2+3^2 + 2× 1000×3

= 1000000 + 9+ 6000

= 1006009 (Ans.)

The second one can also be done by the same method.