Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each expression to its equivalent form.
Expressions:

x2 + 6x + 34
x2 + 16
x2 - 5x + 5
x2 - 12x + 37
x2 + 3x + 15
x2 + 8

Equivalent forms:
(x - 6 + i)(x - 6 - i)

(x + 3 + 5i)(x + 3 - 5i)

(x - 4i)(x + 4i)

Answer 1

Answer:

$x^2 + 6x + 34 = (x + 3 + 5i)(x + 3 - 5i)\\x^2 + 16 = (x - 4i)(x + 4i)\\x^2 - 12x + 37 = (x - 6 + i)(x - 6 - i)$

Step-by-step explanation:

Let us do this starting from the equivalent form

A) $(x - 6 + i)(x - 6 - i)$

Distributing x , -6 and i on the second bracket we get

$x(x - 6 - i)-6(x - 6 - i)+i(x - 6 - i)$

$x^2-6x-ix-6x+36+6i+xi-6i-i^2$

replacing $i^2=-1$

$x^2-6x-6x+36-(-1)$

$x^2-12x+36+1$

$x^2-12x+37$

B) $(x + 3 + 5i)(x + 3 - 5i)$

Distributing x , 3 and 5i on the second bracket we get

$x(x + 3 - 5i)+3(x + 3 - 5i)+5i(x + 3 - 5i)\\x^2+3x-5xi+3x+9-15i+5xi+15i-25i^2\\x^2+3x+3x-5xi+5xi+9-15i+15i-25i^2\\x^2+6x+9-25(-1)\\x^2+6x+9+25\\x^2+6x+34$

C) $(x - 4i)(x + 4i)$

distributing x and 4i on (x+4i)

$x(x + 4i)-4i(x + 4i)\\x^2+4xi-4xi-16i^2\\x^2-16(-1)\\x^2+16$

Answer 2

Answer:

(x + 3 + 5i)(x + 3 - 5i)= x^2 + 6x + 34

(x - 4i)(x + 4i)= x^2 + 16

(x - 6 + i)(x - 6 - i)= x^2 - 12x + 37

Step-by-step explanation: just took the test...