Answer:
18 - 8√2
Step-by-step explanation:
to solve (4 - √2)², we can use FOIL which is:
First
Outside
Inside
Last
we will write the expression 2 times, as it is raised to the 2nd power
(4 - √2)(4 - √2)
so lets start with the F in FOIL:
we multiply 4 × 4
(4 - √2)(4 - √2)
which gives us 16, so that is the start of the simplified expression
now we go to the O in FOIL by multiplying the outside terms of the expression, which are 4 and -√2
(4 - √2)(4 - √2)
this gives us -4√2
the next letter is I in FOIL which is multiplying the inside terms which are again, -√2 and 4
(4 - √2)(4 - √2)
this also gives us -4√2
the last term is L which means we are multiplying the last terms of the expression, which is -√2 x -√2
(4 - √2)(4 - √2)
this gives us 2, as when you multiply a square root by itself it cancels the square root
so the expression we have is:
16 -4√2 -4√2 + 2
combine like terms and we get:
18 -8√2
this cannot be simplified further and this is our answer
