# Can You Solve This Easy Algebra Math Problem?

## Algebra Math Problem: The sum of two variables and the sum of the square of three variables are given. Then find the sum of the fourth power

Solve the following algebra math problem

a+b=1

a^2+b^2=9

a^4+b^4=?

## Solution: we can solve this algebra math problem in two different ways

### Method 1: Using the expansion of (*a* + *b*)^2

We know, *a* + *b* = 1

So,

(*a* + *b*)² = 1 = *a*² + 2*ab* + *b*²

ie,

1 = 9 + 2*ab*

So

*ab* = –4

Then we get

(*a*² + *b*²)² = *a*⁴ + 2*a*²*b*² + *b*⁴

81 = *a*⁴ + *b*⁴ + 2(*ab*)² = *a*⁴ + *b*⁴ + 2 × 16

So

*a*⁴ + *b*⁴ = 49

### Method 2: Using the expansion of (*a* + *b*)^4

We know

(*a* + *b*)⁴ = *a*⁴ + 4*a*³*b* + 6*a*²*b*² + 4*ab*³ + *b*⁴ = *a*⁴ + *b*⁴ + 4*ab*(*a*² + *b*²) + 6*a*²*b*²

1⁴ = *a*⁴ + *b*⁴ + 4(–4) × 9 + 6( –4)²

So

*a*⁴ +* b*⁴ = 49