Question

Evaluate: (-1)^45 × (-1)^102 - (-1)^29​

Answer 1

Answer:

Value of (-1)^45 × (-1)^102 - (-1)^29 is 0

Step-by-step explanation:

Given,

${( -1)}^{45} \times {( - 1)}^{102} - {( - 1)}^{29}$

We know if minus sign has even power then minus becomes plus and if minus sign has odd power then minus becomes minus.

So,

${( -1)}^{45} \times {( - 1)}^{102} - {( - 1)}^{29} \\ = (- 1) \times 1 - ( - 1)$

By Bodmas rule we know,

Bracket-Of- Division - Multiplication - Addition - Subtraction.

So,

$( - 1) \times 1 - ( - 1) \\ = ( - 1) - ( - 1) \\ = - 1 + 1 \\ = 0$

This is a problem of Algebra.

Some important Algebra formulas,

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549