Simplifying Quadratics - GED Math
Card 0 of 8
This is a quadratic equation, but it is not in standard form.
We express it in standard form as follows, using the FOIL technique:
Now factor the quadratic expression on the left. It can be factored as
where 
.
By trial and error we find that 
, so
can be rewritten as
.
Set each linear binomial equal to 0 and solve separately:
The solution set is 
.
This is a quadratic equation, but it is not in standard form.
We express it in standard form as follows, using the FOIL technique:
Now factor the quadratic expression on the left. It can be factored as
where
By trial and error we find that
can be rewritten as
Set each linear binomial equal to 0 and solve separately:
The solution set is
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Subtract:
Subtract:
can be determined by subtracting the coefficients of like terms. We can do this vertically as follows:
By switching the symbols in the second expression we can transform this to an addition problem, and add coefficients:
can be determined by subtracting the coefficients of like terms. We can do this vertically as follows:
By switching the symbols in the second expression we can transform this to an addition problem, and add coefficients:
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Add:
Add:
can be determined by adding the coefficients of like terms. We can do this vertically as follows:
can be determined by adding the coefficients of like terms. We can do this vertically as follows:
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Which of the following expressions is equivalent to the product?
Which of the following expressions is equivalent to the product?
Use the difference of squares pattern
with 
and 
:
Use the difference of squares pattern
with
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Which of the following expressions is equivalent to the product?
Which of the following expressions is equivalent to the product?
Use the difference of squares pattern
with 
and 
:
Use the difference of squares pattern
with
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Simplify:
Simplify:
Start by factoring the numerator. Notice that each term in the numerator has an 
, so we can write the following:
Next, factor the terms in the parentheses. You will want two numbers that multiply to 
and add to 
.
Next, factor the denominator. For the denominator, we will want two numbers that multiply to 
and add to 
.
Now that both the denominator and numerator have been factored, rewrite the fraction in its factored form.
Cancel out any terms that appear in both the numerator and denominator.
Start by factoring the numerator. Notice that each term in the numerator has an
Next, factor the terms in the parentheses. You will want two numbers that multiply to
Next, factor the denominator. For the denominator, we will want two numbers that multiply to
Now that both the denominator and numerator have been factored, rewrite the fraction in its factored form.
Cancel out any terms that appear in both the numerator and denominator.
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Simplify the following expression:
Simplify the following expression:
Start by factoring the numerator.
To factor the numerator, you will need to find 
numbers that add up to 
and multiply to 
.
Next, factor the denominator.
To factor the denominator, you will need to find two numbers that add up to 
and multiply to 
.
Rewrite the fraction in its factored form.
Since 
is found in both numerator and denominator, they will cancel out.
Start by factoring the numerator.
To factor the numerator, you will need to find
Next, factor the denominator.
To factor the denominator, you will need to find two numbers that add up to
Rewrite the fraction in its factored form.
Since
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Simplify:
Simplify:
We need to factor both the numerator and the denominator to determine what can cancel each other out.
If we factor the numerator:
Two numbers which add to 6 and multiply to give you -7.
Those numbers are 7 and -1.
If we factor the denominator:
First factor out a 2 
Two numbers which add to -4 and multiply to give you 3
Those numbers are -3 and -1
Now we can re-write our expression with a product of factors:
We can divide 
and 
to give us 1, so we are left with
We need to factor both the numerator and the denominator to determine what can cancel each other out.
If we factor the numerator:
Two numbers which add to 6 and multiply to give you -7.
Those numbers are 7 and -1.
If we factor the denominator:
First factor out a 2
Two numbers which add to -4 and multiply to give you 3
Those numbers are -3 and -1
Now we can re-write our expression with a product of factors:
We can divide
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