if y1=x^2+3x-1 and y2=x-5,
find: a. y1+y2
b. y1-y2
c. y1(y2)
y1 = x^2 + 3x - 1
y2 = x - 5
for y1 - y2, combine similar terms,, for terms with same variables, add their numerical coefficients (number before the variable) and copy the variable:
x^2 + 3x - 1 -(x - 5)
x^2 + 3x - 1 - x + 5
x^2 + 3x - x - 1 + 5 *i just rearrange the terms*
x^2 + 2x + 4
for y1(y2), distribute each term:
(x^2 + 3x - 1)(x - 5)
to distribute, multiply x^2 by x plus x^2 times -5, plus 3x times x plus 3x times -5, and so on:
(x^2)*x + (-5)x^2 + 3x^2 - 15x - x + 5
now simplify this by combining similar terms.
Alright. a. y1+y2 should be set up as follows:
(x^2+3x-1)+(x-5), which equates to
x^2+4x-6
You just combine the like terms.
b. (x^2+3x-1)-(x-5)
For this one you need to distribute the negative, to get x^2+3x-1-x+5, then combine like terms.
c. (x-5)(x^2+3x-1)= x^3+3x^2-x-5x^2-15x+5. Combine like terms.
To find the value of y1+y2, we need to add the equations y1 and y2 together.
a. y1+y2 = (x^2+3x-1) + (x-5)
To simplify this equation, we combine like terms:
= x^2 + 3x - 1 + x - 5
Now, let's group similar terms together:
= (x^2 + x) + (3x - 1) + (-5)
Finally, we can combine the terms inside each parentheses:
= x(x + 1) + 3x - 1 - 5
Further simplifying gives us:
= x^2 + x + 3x - 6
Combining like terms again:
= x^2 + 4x - 6
Therefore, y1+y2 = x^2 + 4x - 6.
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To find the value of y1-y2, we need to subtract the equation y2 from y1.
b. y1-y2 = (x^2+3x-1) - (x-5)
To simplify this equation, we distribute the negative sign to all terms inside the parentheses:
= x^2 + 3x - 1 - x + 5
Again, group the similar terms together:
= x^2 + 3x - x - 1 + 5
Combine like terms:
= x^2 + 2x + 4
Therefore, y1-y2 = x^2 + 2x + 4.
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To find the value of y1(y2), we need to multiply the equations y1 and y2 together.
c. y1(y2) = (x^2+3x-1)(x-5)
To simplify this equation, we use the distributive property:
= x^2(x-5) + 3x(x-5) - 1(x-5)
Multiplying each term inside parentheses:
= x^3 - 5x^2 + 3x^2 - 15x - x + 5
Combine like terms:
= x^3 - 2x^2 - 16x + 5
Therefore, y1(y2) = x^3 - 2x^2 - 16x + 5.