What is (2x+3) raised to the fifth power

1 answer:

4 0

(2x + 3)⁵
(2x + 3)(2x + 3)(2x + 3)(2x + 3)(2x + 3)(2x + 3)
(2x(2x + 3) + 3(2x + 3))(2x(2x + 3) + 3(2x + 3)(2x + 3)
(2x(2x) + 2x(3) + 3(2x) + 3(3))(2x(2x) + 2x(3) + 3(2x) + 3(3))(2x + 3)
(4x² + 6x + 6x + 9)(4x² + 6x + 6x + 9)(2x + 3)
(4x² + 12x + 9)(4x² + 12x + 9)(2x + 3)
(4x²(4x² + 12x + 9) + 12x(4x² + 12x + 9) + 9(4x² + 12x + 9))(2x + 3)
(4x²(4x²) + 4x²(12x) + 4x²(9) + 12x(4x²) + 12x(12x) + 12x(9) + 9(4x²) + 9(12x) + 9(9))(2x + 3)
(16x⁴ + 48x³ + 36x² + 48x³ + 144x² + 108x + 36x² + 108x + 81)(2x + 3)
(16x⁴ + 48x³ + 48x³ + 36x² + 144x² + 36x² + 108x + 108x + 81)(2x + 3)
(16x⁴ + 96x³ + 216x² + 216x + 81)(2x + 3)
16x⁴(2x + 3) + 96x³(2x + 3) + 216x²(2x + 3) + 216x(2x + 3) + 81(2x + 3)
16x⁴(2x) + 16x⁴(3) + 96x³(2x) + 96x³(3) + 216x²(2x) + 216x²(3) + 216x(2x) + 216x(3) + 81(2x) + 81(3)
32x⁵ + 48x⁴ + 184x⁴ + 288x³ + 432x³ + 648x² + 432x² + 648x + 162x + 243
32x⁵ + 232x⁴ + 720x³ + 1080x² + 810x + 243

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Solving a percent mixture problem using a linear equationSamantha vEspelTwo factory plants are making TV panels. Yesterday, Plan

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ANSWER

Number of panels produced by plant B: 20000

EXPLANATION

First we have to name the variables. We're looking for the number of panels produced by plant B and also we don't know the number of panels produced by plant A.

Let x be the number of panels produced by plant A and y the number of panels produced by plant B.

We know that plant A produced 7000 fewer panels than plant B. This as an equation is:

$x=y-7000$

To solve this we need to find another equation, because we have two variables.

The other equation is the one with the defective panels. The total number of defective panels produced by both plants is 860, and we know that represents the 2% of produced panels from plant A and 3% of produced panels from plant B. To find the number that represents that percentage we divide the percentage by 100 and multiply by the total amount. For the 2% of plant A this is:

$\frac{2}{100}\cdot x=0.02x$

And the 3% of plant B is:

$\frac{3}{100}\cdot y=0.03y$

So the second equation is:

$0.02x+0.03y=860$

Since we only want to find y, which is the number of panels produced by plant B, we can use the substitution method. Substitute the first equation into the second - in other words, replace x in the second equation by y - 7000: