1) (x+8)(x-10)

To find the product of (x+8)(x-10), we can use the identity (a+b)(a-b) = a^2 - b^2.

Let's apply this identity to our expression:

(x+8)(x-10) = x^2 - 10^2

Simplifying further:

= x^2 - 100

So, (x+8)(x-10) simplifies to x^2 - 100.

2) 104 × 96

To find the product of 104 and 96, we can use the identity (a+b)(c+d) = ac + ad + bc + bd.

Let's apply this identity to our expression:

104 × 96 = (100 + 4)(100 - 4)

Using the identity, we can expand this expression:

= 100^2 - 4^2

= 10000 - 16

= 9984

So, 104 × 96 equals 9984.

3) (2x+1)^3

To find the cube of (2x+1), we can use the identity (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.

Let's apply this identity to our expression:

(2x+1)^3 = (2x)^3 + 3(2x)^2(1) + 3(2x)(1)^2 + (1)^3

Expanding further:

= 8x^3 + 3(4x^2) + 6x + 1

= 8x^3 + 12x^2 + 6x + 1

So, (2x+1)^3 simplifies to 8x^3 + 12x^2 + 6x + 1.

4) (2x-yz)^2

To find the square of (2x-yz), we can use the identity (a-b)^2 = a^2 - 2ab + b^2.

Let's apply this identity to our expression:

(2x-yz)^2 = (2x)^2 - 2(2x)(yz) + (yz)^2

Expanding further:

= 4x^2 - 4xyz + y^2z^2

So, (2x-yz)^2 simplifies to 4x^2 - 4xyz + y^2z^2.

5) (102)^3

To find the cube of 102, we can simply multiply 102 by itself twice.

(102)^3 = 102 × 102 × 102

Calculating this:

= 1040406

So, (102)^3 equals 1040406.