Find the following products:
$$(3x-4y+5z)(9{x}^{2}+16{y}^{2}+25{z}^{2}+12xy-15zx+20yz)$$
Given,
$$(3x – 4y + 5z) (9x^2 + 16y^2 + 25z^2 + 12xy – 15zx + 20yz)$$
$$= [3x + (-4y) + 5z] [(3x)^ 2 + (-4y) ^2 + (5z)^ 2 – 3x \times (-4y) -(-4y) (5z) – 5z \times 3x]$$
$$= (3x)^ 3 + (-4y)^ 3 + (5z)^ 3 – 3 \times 3x \times (-4y) (5z)$$
$$= 27x^3 – 64y^3 + 125z^3 + 180xyz$$