Find the following products:$(3x -4y + 5z) (9x^2 + 16y^2 + 25z^2 + 12xy- 15zx + 20yz)$

Given: 

$(3x -4y + 5z) (9x^2 + 16y^2 + 25z^2 + 12xy- 15zx + 20yz)$

To do: 

We have to find the given product.

Solution: 

We know that

$(a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc$

Therefore,

$(3x – 4y + 5z) (9x^2 + 16y^2 + 25z^2 + 12xy – 15zx + 20yz)= [3x + (-4y) + 5z] [(3x)^2 + (-4y)^2 + (5z)^2 – 3x \times (-4y) -(-4y) \times (5z) – 5z \times 3x]$

$= (3x)^3 + (-4y)^3 + (5z)^3 – 3 \times 3x \times (-4y) \times (5z)$

$= 27x^3 – 64y^3 + 125z^3 + 180xyz$

Hence, $(3x – 4y + 5z) (9x^2 + 16y^2 + 25z^2 + 12xy – 15zx + 20yz)=27x^3 – 64y^3 + 125z^3 + 180xyz$.

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Updated on: 10-Oct-2022

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