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(sqrt(x) + 7) * (sqrt(x) - 7) is solved using the distributive law of algebraic operations as follows:
\n" ); document.write( "(sqrt(x) + 7) * (sqrt(x) - 7) is equal to:
\n" ); document.write( "(sqrt(x) * (sqrt(x) - 7)) + 7 * (sqrt(x) - 7) which becomes:
\n" ); document.write( "sqrt(x) * sqrt(x) - 7 * sqrt(x) + 7 * sqrt(x) - 49
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "sqrt(x) * sqrt(x) - 49 which becomes:
\n" ); document.write( "(sqrt(x))^2 - 49 which becomes:
\n" ); document.write( "x - 49
\n" ); document.write( "this is because sqrt(x) * sqrt(x) is equal to (sqrt(x))^2 is equal to x.
\n" ); document.write( "this might be seen clearer if you use exponent arithmetic.
\n" ); document.write( "sqrt(x) is equal to x^(1/2)
\n" ); document.write( "sqrt(x) * sqrt(x) is therefore equal to:
\n" ); document.write( "x^(1/2) * x^(1/2)
\n" ); document.write( "by the laws of exponent arithmetic, this becomes:
\n" ); document.write( "x^((1/2) + (1/2)) which becomes x^1 which becomes x.
\n" ); document.write( "the whole thing might be easier to see if you allow:
\n" ); document.write( "y = sqrt(x).
\n" ); document.write( "your equation of:
\n" ); document.write( "(sqrt(x)+7) * (sqrt(x)-7) becomes:
\n" ); document.write( "(y+7)*(y-7)
\n" ); document.write( "you can use foil or you can use the distributive property of arithmetic (foil is just a subset of the distributive property) to get:
\n" ); document.write( "y^2 - 7y + 7y - 49
\n" ); document.write( "the -7y and the + 7y cancel out and you are left with:
\n" ); document.write( "y^2 - 49
\n" ); document.write( "since y = sqrt(x), then y^2 = x and you are left with:
\n" ); document.write( "x - 49.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "