Answer:

To simplify the expression, let's break it down step by step:

16 × 2^(n + 1) - 4 × 2^2 - 16 × 2^(n + 2) - 2 × 2^(n + 2)

First, let's simplify the terms with the same base, which is 2:

16 × 2^(n + 1) can be written as 2^4 × 2^(n + 1) = 2^(4 + n + 1) = 2^(n + 5)

-4 × 2^2 can be written as -4 × 4 = -16

-16 × 2^(n + 2) can be written as -2^4 × 2^(n + 2) = -2^(4 + n + 2) = -2^(n + 6)

-2 × 2^(n + 2) can be written as -2 × 2^2 × 2^(n) = -4 × 2^(n + 2) = -4 × 2^(n + 2)

Now, let's put it all together:

2^(n + 5) - 16 - 2^(n + 6) - 4 × 2^(n + 2)

We can observe that both terms 2^(n + 5) and -2^(n + 6) have a common base of 2, so we can combine them:

2^(n + 5) - 2^(n + 6) can be written as 2^(n + 5) - 2 × 2^(n + 5) = 2^(n + 5) - 2^(n + 5 + 1) = 2^(n + 5) - 2^(n + 6)

Now, let's simplify further:

2^(n + 5) - 2^(n + 6) - 16 - 4 × 2^(n + 2)

The expression can be simplified by combining like terms:

2^(n + 5) - 2^(n + 6) can be written as -2^(n + 6) - 16 + 2^(n + 5) - 4 × 2^(n + 2)

This is the simplified form of the expression.

Verified answer

Step-by-step explanation:

16×2

n+2

−2×2

n+2

16×2

n+1

−4×2

n

=

16×2

2

×2

n

−2×2

2

×2

n

16×2×2

n

−4×2

2n

(asa

m+n

=a

m

−a

n

)

=

2

n

(16×2

2

−2×2

2

)

2

n

(16×2−4)

=

16×4−2×4

32−4

=

56

28

=

2

1