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Factoring A Difference Between Two Squares

Examine the problem / expression below:

-9 + j4

Again, the first step at factoring this expression is to verify that the expression is a Difference Between Two Squares.

Question Answer and Reason
Are there only two terms? Yes. The first term is -9; the second term is j4.
Are both coefficients (9 and 1) perfect squares? Yes. Notice 3 times 3 equals 9 and 1 times 1 equals 1.
Are all of the variables in the expression raised to an even (2,4,6, ...) power? Yes. There is only one variable, j, and it has a power of 4 which is even.
Does one term have a positive coefficient, and another term have a negative coefficient? Yes. The coefficient 1 is positive, the coefficient -9 is negative.

Unlike the last problem, the first term is negative. To make factoring this expression easier, simply switch the two terms so that the negative term is second.

-9 + j4

becomes

j4 - 9

Now, continue factoring as in the last problem. Write two sets of open parentheses:

(                )(                )

Find the square root of the first term, j4. Write the result, j2, on the left inside of each set of parentheses.

( j2           )( j2           )

Find the square root of the second term, 9. Write the result, 3, on the right inside of each set of parentheses.

( j2          3)( j2          3)

Now write a plus sign in the middle of the first set of parentheses and write a minus sign in the middle of the second set of parentheses.

( j2     +     3)( j2    -      3)

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