Respuesta:
Explicación paso a paso:
Let's solve each equation step by step:
### a) \( (5x - 4)(2x - 3) - 5 = \)
First, expand the product:
\[ (5x - 4)(2x - 3) = 5x \cdot 2x + 5x \cdot (-3) + (-4) \cdot 2x + (-4) \cdot (-3) \]
\[ = 10x^2 - 15x - 8x + 12 \]
\[ = 10x^2 - 23x + 12 \]
Then, subtract 5:
\[ 10x^2 - 23x + 12 - 5 \]
\[ = 10x^2 - 23x + 7 \]
So, the solution is:
\[ 10x^2 - 23x + 7 \]
### b) \( 3(x^2 + 5) - (x^2 + 40) = \)
First, distribute 3 in the first term:
\[ 3(x^2 + 5) = 3x^2 + 15 \]
Then, subtract the second term:
\[ 3x^2 + 15 - (x^2 + 40) \]
\[ = 3x^2 + 15 - x^2 - 40 \]
\[ = 2x^2 - 25 \]
So, the solution is:
\[ 2x^2 - 25 \]
### c) \( x \cdot (5x - 4) - 2 \cdot (x^2 - x) = \)
First, distribute \( x \) in the first term:
\[ x(5x - 4) = 5x^2 - 4x \]
Then, distribute \( 2 \) in the second term:
\[ 2(x^2 - x) = 2x^2 - 2x \]
Now, subtract the second term from the first:
\[ 5x^2 - 4x - (2x^2 - 2x) \]
\[ = 5x^2 - 4x - 2x^2 + 2x \]
\[ = 3x^2 - 2x \]
So, the solution is:
\[ 3x^2 - 2x \]
### d) \( x^2 - (x - 1)^2 = \)
First, expand \( (x - 1)^2 \):
\[ (x - 1)^2 = x^2 - 2x + 1 \]
Then, subtract this from \( x^2 \):
\[ x^2 - (x^2 - 2x + 1) \]
\[ = x^2 - x^2 + 2x - 1 \]
\[ = 2x - 1 \]
So, the solution is:
\[ 2x - 1 \]
### e) \( 3x^2 - 2(x + 5) - (x + 3) = \)
First, distribute \( 2 \) in the second term:
\[ -2(x + 5) = -2x - 10 \]
Then, distribute the negative sign in the third term:
\[ -(x + 3) = -x - 3 \]
Now, combine all terms:
\[ 3x^2 - 2x - 10 - x - 3 \]
\[ = 3x^2 - 3x - 13 \]
So, the solution is:
\[ 3x^2 - 3x - 13 \]
### f) \( 3x^2 - 2(x + 5) - (x + 3) + 19 = \)
First, distribute \( 2 \) in the second term:
\[ -2(x + 5) = -2x - 10 \]
Then, distribute the negative sign in the third term:
\[ -(x + 3) = -x - 3 \]
Now, combine all terms including the constant:
\[ 3x^2 - 2x - 10 - x - 3 + 19 \]
\[ = 3x^2 - 3x + 6 \]
So, the solution is:
\[ 3x^2 - 3x + 6 \]
### g) \( x^2 - 4(x^2 + 3x - 1) = \)
First, distribute \( 4 \) in the second term:
\[ 4(x^2 + 3x - 1) = 4x^2 + 12x - 4 \]
Then, subtract this from \( x^2 \):
\[ x^2 - (4x^2 + 12x - 4) \]
\[ = x^2 - 4x^2 - 12x + 4 \]
\[ = -3x^2 - 12x + 4 \]
So, the solution is:
\[ -3x^2 - 12x + 4 \]
