AlgebraFactoring Perform the indicated operations and put in

Algebra-Factoring

Perform the indicated operations and put in descending order if needed.

#1   (8x^2+3x+5)+(-5x+3)

#2   (2x^2+3)(3x^2+5)

#3   (n-5)^2

Solution

1) (8x² + 3x + 5) + (-5x + 3)

==> 8x² + 3x + 5 - 5x + 3

==> 8x² - 2x + 8

Hence (8x² + 3x + 5) + (-5x + 3) = 8x² - 2x + 8

2) (2x² + 3)(3x² + 5)

==> 2x²(3x²) + 2x²(5) + 3(3x²) + 3(5)

==> 6x²⁺² + 10x² + 9x² + 15              ; since a^m aⁿ = a^m+n

==> 6x⁴ + 19x² + 15

Hence (2x² + 3)(3x² + 5) = 6x⁴ + 19x² + 15

3) (n - 5)²

==> n² - 2(n)(5) + 5²    ; since (a - b)² = a² - 2ab + b²

==> n² - 10n + 25

Hence (n - 5)² = n² - 10n + 25