Simplifying Polynomials
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Math › Simplifying Polynomials
Multiply the expressions:
Explanation
You can look at this as the sum of two expressions multiplied by the difference of the same two expressions. Use the pattern
,
where and
.
To find , you use the formula for perfect squares:
,
where and
.
Substituting above, the final answer is .
Simplify the following polynomial:
Explanation
Begin by reversing the numerator and denominator so that the exponents are positive:
Square the right side of the expression and multiply:
Simplify:
Simplify the following polynomial:
Explanation
To simplify the polynomial, begin by multiplying the first binomial by every term within the parentheses:
Now, combine like terms:
Convert the polynomial into fraction form:
Multiply:
Explanation
If and
, what is
?
Explanation
is a composite function solved by substituting
into
:
Divide the trinomial below by .
Explanation
We can accomplish this division by re-writing the problem as a fraction.
The denominator will distribute, allowing us to address each element separately.
Now we can cancel common factors to find our answer.
Simplify the following polynomial:
Explanation
Begin by simplifying the integers:
Subtract the exponent in the denominator from the exponent in the numerator:
Simplify the following polynomial:
Explanation
To simplify the polynomial, begin by rearranging the terms to have positive exponents:
Now, combine like terms:
Simplify the integers:
Simplify the following polynomial:
Explanation
Begin by multiplying the terms:
Convert into fraction form:
Simplify the following expression.
Explanation
This is not a FOIL problem, as we are adding rather than multiplying the terms in parenteses.
Add like terms to solve.
Combining these terms into an expression gives us our answer.