Question

Expand the following:

(3x + y – 5z)²

Answer 1

Given: (3x + y – 5z)²

Step-wise calculation:

We use the algebraic identity for the square of a trinomial:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca 

Here, a = 3x, b = y and c = –5z.

Calculate each term:

a² = (3x)² = 9x²

b² = y²

c² = (–5z)² = 25z²

Calculate the cross terms:

2ab = 2 × (3x) × y = 6xy

2bc = 2 × y × (–5z) = –10yz

2ca = 2 × (–5z) × (3x) = –30xz

Combine all terms:

(3x + y – 5z)² = 9x² + y² + 25z² + 6xy – 10yz – 30xz