Explanation

Given: (x + 1/x)(x − 1/x)

Use the formula for difference of squares:  

(a + b)(a − b) = a² − b²

Here, a = x and b = 1/x

So, (x + 1/x)(x − 1/x) = x² − (1/x)²  

= x² − 1/x²

Explanation

We are given the expression:

100² − 99²

This is a difference of squares:

a² − b² = (a − b)(a + b)

So:

100² − 99² = (100 − 99)(100 + 99) = 1 × 199 = 199

Explanation

The standard form of a quadratic equation is ax^2 + bx + c = 0.

It represents a quadratic polynomial set equal to zero, where a, b, and c are constants.

Explanation

Given: y = (2x + 3)⁴  

Using the chain rule:  

dy/dx = 4(2x + 3)³ * d/dx(2x + 3)  

= 4(2x + 3)³ * 2  

= 8(2x + 3)³  

Explanation

We simplify the expression:

x(x⁵)⁴ / x⁴

Step 1: Simplify the exponent  

(x⁵)⁴ = x^(5×4) = x²⁰

Now the expression becomes:  

x × x²⁰ / x⁴

Step 2: Combine the exponents  

Numerator: x × x²⁰ = x²¹  

Now divide: x²¹ / x⁴ = x^(21−4) = x¹⁷