Question

simplify the following
$(x - 1)(4x - 3)$
$\frac{-8x^{5} + 28x^{4}-4x^{3}}{4x^{3}}$
$\frac{x^{2} - 12x + 20}{x - 2}$
$-4y(5y - 11) - 2y(3y + 10)$

Explanation:

Problem 1: $(x-1)(4x-3)$

Step1: Apply distributive property (FOIL)

$x(4x) + x(-3) -1(4x) -1(-3)$

Step2: Calculate each term

$4x^2 -3x -4x +3$

Step3: Combine like terms

$4x^2 + (-3x-4x) +3 = 4x^2 -7x +3$

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Problem 2: $\frac{-8x^5 +28x^4 -4x^3}{4x^3}$

Step1: Split into individual fractions

$\frac{-8x^5}{4x^3} + \frac{28x^4}{4x^3} - \frac{4x^3}{4x^3}$

Step2: Simplify each fraction

$-2x^{5-3} +7x^{4-3} -1$

Step3: Simplify exponents

$-2x^2 +7x -1$

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Problem 3: $\frac{x^2 -12x +20}{x-2}$

Step1: Factor the numerator

$x^2 -12x +20 = (x-2)(x-10)$

Step2: Cancel common factors

$\frac{(x-2)(x-10)}{x-2} = x-10$ (where $x
eq 2$)

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Problem 4: $-4y(5y-11)-2y(3y+10)$

Step1: Distribute the coefficients

$-4y(5y) + (-4y)(-11) -2y(3y) -2y(10)$

Step2: Calculate each term

$-20y^2 +44y -6y^2 -20y$

Step3: Combine like terms

$(-20y^2-6y^2) + (44y-20y) = -26y^2 +24y$

Answer:

1. $4x^2 -7x +3$
2. $-2x^2 +7x -1$
3. $x-10$ (where $x

eq 2$)

1. $-26y^2 +24y$