Which expressions are equivalent to 2(2x + 4y + x − 2y)?

Mathematics

1 answer:

joja [24]3 years ago

7 0

Answer: 2(3x + 2y) and 6x + 4y

Step-by-step explanation:

Hi, to answer this question we have to solve the expression.

2(2x + 4y + x − 2y)

First we have to simplify the expression within the brackets.

2 (2x + x +4y -2y)

2( 3x + 2y)

We have the first equivalent expression. Now to obtain the second expression we apply distributive property:

2 (3x) + 2 ( 2y)

6x + 4y

In conclusion 2(3x + 2y) and 6x + 4y are equivalent expressions to 2(2x + 4y + x − 2y).

Feel free to ask for more if it´s necessary or if you did not understand something.

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Step-by-step explanation:

Your expression is

$\sqrt [3] {-54x^{5}y^{6}}$

Here's how I would simplify it.

$\begin{array}{rcll}\sqrt [3] {-54x^{5}y^{6}} & = & \sqrt [3] {(-1)^{3}\times 2 \times 27 \times x^{2} \times x^{3} \times y^{6}} & \text{Factored the cubes}\\& = & \sqrt [3] {(-1)^{3} \times 3^{3}\times x^{3} \times y^{6}\times 2 \times x^{2}} & \text{Grouped the cubes}\\\end{array}$

$\begin{array}{rcll}& = & \sqrt [3] {(-1)^{3} \times {3^{3}\times x^{3} \times y^{6}}} \times\sqrt [3] { 2 \times x^{2}} & \text{Separated the cubes}\\&=& \mathbf{-3xy^{2}\sqrt [3] {2x^{2}}} & \text{Took cube roots}\\\end{array}$