Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Answer 1

Answer:

(x + 1 + i)(x + 1 - i) ↔ x²+2x+2; (x+2i)(x-2i) ↔ x²+4; (x-2i-2)(x+2i-2) ↔ x²-4x+8

Explanation:

For the first expression, use the distributive property to multiply.  First multiply all terms of the second trinomial by x:

x(x)+x(1)-x(i) = x²+x-xi

Next multiply all terms of the second trinomial by 1:

1(x)+1(1)-1(i) = x+1-i

Next multiply all terms of the second trinomial by i:

i(x)+i(1)-i(i) = xi+i-i²

Combining all terms,

x²+x-xi+x+1-i+xi+i-i²

Combining like terms, we have

x²+(x+x)+(-xi+xi)+(-i+i)+1-i² = x²+2x+1-i² = x²+2x+1-(-1) = x²+2x+2

For the second expression, use the acronym FOIL (First, Outer, Inner, Last):

x(x) = x²

x(-2i) = -2xi

2i(x) = 2xi

2i(-2i) = -4i² = -4(-1) = 4

This gives us x² - 2xi + 2xi + 4, which simplifies to x²+4.

For the third expression, use the distributive property.  Multiply everything in the second trinomial by x:

x(x)+x(2i)+x(-2) = x²+2xi-2x

Multiply everything in the second trinomial by -2i:

-2i(x)+-2i(2i)+-2i(-2) = -2xi-4i²+4i = -2xi-4(-1)+4i = -2xi+4+4i

Multiply everything in the third trinomial by -2:

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

Combining all, we have

x²+2xi-2x+-2xi+4+4i+-2x-4i+4

Combining like terms gives us

x²+(2xi+-2xi)+(-2x+-2x)+(4+4)+(4i-4i) = x²-4x+8

Answer 2

The first one is x^2+2x+2
the second one is x^2+4
the last one is x^2-4x+8