Simplifying Polynomials

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Math › Simplifying Polynomials

Questions 1 - 10
1

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 .

2

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:

3

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:

4

Multiply:

Explanation

5

If and , what is ?

Explanation

is a composite function solved by substituting into :

6

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.

7

Simplify the following polynomial:

Explanation

Begin by simplifying the integers:

Subtract the exponent in the denominator from the exponent in the numerator:

8

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:

9

Simplify the following polynomial:

Explanation

Begin by multiplying the terms:

Convert into fraction form:

10

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.

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