document.write( "Question 203415: Use the difference of two squares theorem to find the solution to the equations b squared = 18 and z squared = 13 \n" ); document.write( "

Algebra.Com's Answer #153469 by jsmallt9(3758) $\"\"$ $\"About$

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Difference of two squares: $\"a%5E2+-+b%5E2+=+%28a+%2B+b%29%28a+-+b%29\"$
\n" ); document.write( " $\"b%5E2+=+18\"$
\n" ); document.write( "First let's get a difference by subtracting 18 from both sides:
\n" ); document.write( " $\"b%5E2+-+18+=+0\"$
\n" ); document.write( "Now we need to write this as a difference of squares. b^2 is already a square. Next we need to write 18 as a square. What squared is 18? Answer: $\"sqrt%2818%29\"$ . Now we have:
\n" ); document.write( " $\"b%5E2+-+%28sqrt%2818%29%29%5E2+=+0\"$
\n" ); document.write( "which is a difference of squares. We can rewrite this as:
\n" ); document.write( " $\"%28b+%2B+sqrt%2818%29%29%28b+-+sqrt%2818%29%29+=+0\"$
\n" ); document.write( "In order for this (or any) product to be zero, one of the factors must be zero (Zero Product Property). So
\n" ); document.write( " $\"b+%2B+sqrt%2818%29+=+0\"$ or $\"b+-+sqrt%2818%29+=+0\"$
\n" ); document.write( "Solving these we get:
\n" ); document.write( " $\"b+=+-sqrt%2818%29\"$ or $\"b+=+sqrt%2818%29\"$
\n" ); document.write( "We can simplify these square roots.
\n" ); document.write( " $\"sqrt%2818%29+=+sqrt%289%2A2%29+=+sqrt%289%29%2Asqrt%282%29+=+3sqrt%282%29\"$
\n" ); document.write( "So the simplified answers:
\n" ); document.write( " $\"b+=+-3sqrt%282%29\"$ or $\"b+=+3sqrt%282%29\"$

\n" ); document.write( "Using the same steps on $\"z%5E2+=+13\"$ we get $\"z+=+sqrt%2813%29\"$ or $\"z+=+-sqrt%2813%29\"$ \n" ); document.write( "

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