How to subtract polynomials - ACT Math
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Simplify:
Simplify:
When subtracting polynomials, it's helpful to remember that the "minus sign" gets distributed. It's as if the two polynomials are being added and a -1 is in front of the second polynomial.
This -1 will get multiplied to all the terms in the second polynomial that is being subtracted from the first, so it becomes 
. You may note that by multiplying by -1, every term in the polynomial switches its original sign. The problem then becomes:
From here, in order to simplify, because there's no equal sign, it can be deduced that we are not working toward a solution for x. The original problem is presented as an expression so an expression as an answer will be expected. In order to work towards a final simplified expression, like terms must be collected. This will provide the final answer.
When subtracting polynomials, it's helpful to remember that the "minus sign" gets distributed. It's as if the two polynomials are being added and a -1 is in front of the second polynomial.
This -1 will get multiplied to all the terms in the second polynomial that is being subtracted from the first, so it becomes
From here, in order to simplify, because there's no equal sign, it can be deduced that we are not working toward a solution for x. The original problem is presented as an expression so an expression as an answer will be expected. In order to work towards a final simplified expression, like terms must be collected. This will provide the final answer.
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Simplify:
Simplify:
Begin by distributing the subtraction of the second term in this question:
Now, you merely need to combine like terms:
Begin by distributing the subtraction of the second term in this question:
Now, you merely need to combine like terms:
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The expression 
is equivalent to which of the following?
The expression
To answer this question, we must distribute the 
to the rest of the variables 
, 
, and 
that are within the brackets.
To distribute a variable or number, you multiply that value with every other value within the brackets or parentheses. So, for this data:
We then simplify the expression by combining the variables we are multiplying together into expressions. For this data:
Be sure to keep all of your operations the same within the problem itself, unless the number being distributed is negative, which will then switch the signs with the brackets from positive to negative or negative to positive.
Therefore, our answer is 
.
To answer this question, we must distribute the
To distribute a variable or number, you multiply that value with every other value within the brackets or parentheses. So, for this data:
We then simplify the expression by combining the variables we are multiplying together into expressions. For this data:
Be sure to keep all of your operations the same within the problem itself, unless the number being distributed is negative, which will then switch the signs with the brackets from positive to negative or negative to positive.
Therefore, our answer is
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Solve the equation 
Solve the equation
To answer this question, we are solving for the values of 
that make this equation true.
To this, we need to get 
on a side by itself so we can evaluate it. To do this, we first add 
to both sides so that we can then begin to deal with the 
value. So, for this data:
can also be written as 
. Therefore:
Now we can divide both sides by 
and find the value of 
.
Therefore, the answer to this question is 
To answer this question, we are solving for the values of
To this, we need to get
Now we can divide both sides by
Therefore, the answer to this question is
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If 
, then what does 
equal?
If
To solve this equation, we substitute 
in for every instance of 
seen in the original equation 
.
Therefore the new equation would read
Now we must square the expression 
. To do this, you must multiply the expression by itself. Therefore:
We must now plug in our new value for 
into our original equation in place of 
.
Now we must distribute the 
into 
. To do this, you multiply each expression within the parenthesis by 
:
Therefore, our answer is 
.
To solve this equation, we substitute
Therefore the new equation would read
Now we must square the expression
We must now plug in our new value for
Now we must distribute the
Therefore, our answer is
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