# Evaluate: 6x^2-12x-48=0

## Expression: ${\left( 2x+8y-4z \right)}^{3}$

Use ${\left( a+b+c \right)}^{3}={a}^{3}+{b}^{3}+{c}^{3}+3 \times {a}^{2}b+3 \times {a}^{2}c+3 \times {b}^{2}a+3 \times {b}^{2}c+3 \times {c}^{2}a+3 \times {c}^{2}b+6 \times abc$ to expand the expression

${\left( 2x \right)}^{3}+{\left( 8y \right)}^{3}+{\left( -4z \right)}^{3}+3 \times {\left( 2x \right)}^{2} \times 8y+3 \times {\left( 2x \right)}^{2} \times \left( -4 \right)z+3 \times {\left( 8y \right)}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+{\left( 8y \right)}^{3}+{\left( -4z \right)}^{3}+3 \times {\left( 2x \right)}^{2} \times 8y+3 \times {\left( 2x \right)}^{2} \times \left( -4 \right)z+3 \times {\left( 8y \right)}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}+{\left( -4z \right)}^{3}+3 \times {\left( 2x \right)}^{2} \times 8y+3 \times {\left( 2x \right)}^{2} \times \left( -4 \right)z+3 \times {\left( 8y \right)}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times {\left( 2x \right)}^{2} \times 8y+3 \times {\left( 2x \right)}^{2} \times \left( -4 \right)z+3 \times {\left( 8y \right)}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times {\left( 2x \right)}^{2} \times \left( -4 \right)z+3 \times {\left( 8y \right)}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times {\left( 8y \right)}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times {\left( 8y \right)}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times {\left( -4z \right)}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times {\left( -4z \right)}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

To raise a product to a power, raise each factor to that power

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y+6 \times 2x \times 8y \times \left( -4 \right)z$

Multiplying an odd number of negative terms makes the product negative

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-6 \times 2x \times 8y \times 4z$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+3 \times 4{x}^{2} \times 8y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y+3 \times 4{x}^{2} \times \left( -4 \right)z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Multiplying an odd number of negative terms makes the product negative

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-3 \times 4{x}^{2} \times 4z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-48{x}^{2}z+3 \times 64{y}^{2} \times 2x+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-48{x}^{2}z+384x{y}^{2}+3 \times 64{y}^{2} \times \left( -4 \right)z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Multiplying an odd number of negative terms makes the product negative

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-48{x}^{2}z+384x{y}^{2}-3 \times 64{y}^{2} \times 4z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-48{x}^{2}z+384x{y}^{2}-768{y}^{2}z+3 \times 16{z}^{2} \times 2x+3 \times 16{z}^{2} \times 8y-384xyz$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-48{x}^{2}z+384x{y}^{2}-768{y}^{2}z+96x{z}^{2}+3 \times 16{z}^{2} \times 8y-384xyz$

Calculate the product

$8{x}^{3}+512{y}^{3}-64{z}^{3}+96{x}^{2}y-48{x}^{2}z+384x{y}^{2}-768{y}^{2}z+96x{z}^{2}+384y{z}^{2}-384xyz$

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