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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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