Calculate

(X+1)(x+2)²
Simplify

1 answer

First, let's expand the expression:

(X+1)(x+2)² = (X+1)(x+2)(x+2)
= (X+1)(x² + 2x + 2x + 4)
= X(x² + 4x + 4) + 1(x² + 4x + 4)
= Xx² + 4Xx + 4X + x² + 4x + 4

Simplifying further, we get:
= Xx² + x² + 4Xx + 4x + 4X + 4
= x²(X + 1) + 4x(X + 1) + 4(X + 1)
= (X + 1)(x² + 4x + 4)
= (X + 1)(x + 2)²

Therefore, the simplified expression is (X + 1)(x + 2)².