Question

Factorise: 6xy(a² + b²) + 8yz(a² + b²) −10xz(a² + b²)

Answer 1

6xy(a² + b²) + 8yz(a² + b²) − 10xz(a² + b²)

Since (a² + b²) is common in all three terms, factor it out:

(6xy + 8yz − 10xz)(a² + b²)

Now the expression is:

(6xy + 8yz − 10xz)(a² + b²)

Factorize the trinomial 6xy + 8yz − 10xz

6xy + 8yz − 10xz = 2y(3x + 4z) − 2z(5x).

y(3x + 4z) − 2z(5x) = 2(3x + 4z)(y − z).

The fully factorized form of the original expression is:

2(3x + 4z)(y − z)(a² + b²)