Please help expand the expression using pascal's triangle (1-2x)^4

2 answers:

7 0

Expanding (1-2x)⁴ would get you something like

 ? (-2x)⁰1⁴ + ? (-2x)¹ 1³ + ? (-2x)² 1² + ? (-2x)³ 1¹ + ? (-2x)⁴ 1⁰

 ? - ? 2x + ? 4x² - ? 8x³ + ? 16x⁴

Fourth row in pascal triangle would be

1, 4, 6, 4, 1

So you insert these numbers in " ? "

1 - 4·2x + 6·4x² - 4·8x³ + 1·16x⁴

Simplify a little more;

(1-2x)⁴ = 1 - 8x + 24x² - 32x³ + 16x⁴

aliya0001 [1]3 years ago

5 0

(1 - 2x)⁴
(1 - 2x)(1 - 2x)(1 - 2x)(1 - 2x)
[1(1 - 2x) - 2x(1 - 2x)][1(1 - 2x) - 2x(1 - 2x)]
[1(1) - 1(2x) - 2x(1) - 2x(-2x)][1(1) - 1(2x) - 2x(1) - 2x(-2x)]
(1 - 2x - 2x + 4x²)(1 - 2x - 2x + 4x²)
(1 - 4x + 4x²)(1 - 4x + 4x²)
1(1 - 4x + 4x²) - 4x(1 - 4x + 4x²) + 4x²(1 - 4x + 4x²)
1(1) - 1(4x) + 1(4x²) - 4x(1) - 4x(-4x) - 4x(4x²) + 4x²(1) - 4x²(4x) + 4x²(4x²)
1 - 4x + 4x² - 4x + 16x² - 16x³ + 4x² - 16x³ + 16x⁴
1 - 4x - 4x + 4x² + 16x² + 4x² - 16x³ - 16x³ + 16x⁴
1 - 8x + 24x² - 32x³ + 16x⁴

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Trava [24]

Answer:

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Step-by-step explanation:

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3 0

2 years ago

The graph of a linear relationship has a slope of -5 and passes through the point (2, -12). Write the equation of the line in sl

DerKrebs [107]

<h3>Answer:</h3>

y=-5x-2

<h3>Solution:</h3>

We are given the line's slope and a point that it passes through.
Using the given information, we can write the equation of the line in Point-Slope Form:
$y-y_1=m(x-x_1)$
In this formula, y₁ stands for the y-coordinate of the point, m stands for the slope of the line, and x₁ stands for the x-coordinate of the point.
In this case, y₁ is equal to -12, m is equal to -5, and x₁ is equal to 2.
Plug in the values:
y-(-12)=-5(x-2)
y+12=-5(x-2)
Now, convert into Slope-Intercept Form, y=mx+b:
y+12=-5x+10
y=-5x+10-12
y=-5x-2