Question

Rewrite each expression as a polynomial in standard form.a)(x+i)(x-i)b)(x+5i)(x-5i)

Answer 1

a) x² +1

b) x² +25

Explanation:

a) (x+i)(x− i)

= x² - ( i ) x + ( i ) x - ( i)²

= x² - i² ∵ i² = -1

= x² - (-1)

= x² +1

b) (x+5 i)(x− 5i)

= x² - ( 5 i ) x + ( 5 i ) x - ( 5 i)²

= x² - 25 i² ∵ i² = -1

= x² - 25(-1)

= x² +25

we can also solve

using identity

(a + b)(a - b) = a² - b²

= (x+5 i)(x− 5i)

= x² - (5 i)²

= x² - 25 i²

= x² +25