Perform the indicated operations simplifying whenever possib

Perform the indicated operations, simplifying whenever possible and expressing the answer in standard form: (x + 7)(x^2 - 7x + 49) (x^3 - 7x^2 - 49x + 343 x^2 +49 x^3 - 343 x^3 + 343 None of these answers. Perform the indicated operations, simplifying whenever possible and expressing the answer in standard form: (x^2 - 4)(x^2 - 25) x^4 - 29 x^4 + 29x^2 +100 x^4 - 29x^2 +100 x^2 - 29x + 100 x^2+29x + 100 x^4 +29 None of these answers Evaluate the radical, simplifying or combining like radicals when possible: (squareroot 45 - squareroot 80)(squareroot 45 + squareroot 80) squareroot 5 -squareroot 5 35 -35 125 -125 25 squareroot 5 24 squareroot 5 23 squareroot 5 None of these answers

Solution

1) (x + 7)(x² - 7x + 49)

==> x(x² - 7x + 49) + 7(x² - 7x + 49)

==> x²⁺¹ - 7x¹⁺¹ + 49x + 7x² - 49x + 343 ; since a^m aⁿ = a^m+n

==> x³ - 7x² + 49x + 7x² - 49x + 343

==> x³ + 343

==> (x + 7)(x² - 7x + 49) = x³ + 343 (option i)

2) (x² - 4) (x² - 25)

==> x²(x² - 25) - 4(x² - 25)

==> x²⁺² - 25x² - 4x² + 100 ; since a^m aⁿ = a^m+n

==> x⁴ - 29x² + 100

Hence (x² - 4) (x² - 25) = x⁴ - 29x² + 100 (option C)

3) (45 - 80)(45 + 80)

==> (45)² - (80)² ; since (a - b)(a + b) = a² - b²

==> (45^1/2)² - (80^1/2)²

==> 45^(1/2)(2) - 80^(1/2)(2)       ; since (a^m)ⁿ = a^mn

==> 45 - 80

==> -35

Hence (45 - 80)(45 + 80) = -35 (option d)