document.write( "Question 588700: Hi, I am studying for my college placement test and there is a few math problems that i am having difficulty solving, \r
\n" ); document.write( "\n" ); document.write( "1st. square root of 75/2 + cube root of 2/4 =\r
\n" ); document.write( "\n" ); document.write( "2nd. 1/2(n^2) - n = 190 my answer was n2-n-380=0 but i think is wrong the answer must equal 0\r
\n" ); document.write( "\n" ); document.write( "3rd. 10x^2+5x/5x my answer was 10x^2 but i think is wrong\r
\n" ); document.write( "\n" ); document.write( "4th. how to factor 3x^2-15x, the correct answer is 3x(x-5) but i dont know why or how they get those numbers\r
\n" ); document.write( "\n" ); document.write( "5th. (4x-7)^2= ? my answer was 16x^2+49 but i think is wrong \n" ); document.write( "
Algebra.Com's Answer #374737 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
Once you are accepted, it may not be a bad idea to be placed in a lower level math class, if that class helps you understand math. Of course, that depends on the teacher. Some people believe math is a difficult subject, mastered by memorizing formulas and procedures. I believe math is about understanding the meaning (and memorizing) a few definitions, and using your own reasoning to get the rest.
\n" ); document.write( "1) \"sqrt%2875%2F2%29+%2B+root%283%2C2%2F4%29\" = ?
\n" ); document.write( "For roots, the root of a product equals the product of the roots, and the root of a quotient is the quotient of the roots.
\n" ); document.write( "\"sqrt%2875%2F2%29=sqrt%2875%29%2Fsqrt%282%29\" and \"root%283%2C2%2F4%29=root%283%2C2%29%2Froot%283%2C4%29\", but those expressions are not the simplified forms expected.
\n" ); document.write( "To make things simple (and pretty), we do a lot of clever factoring, like
\n" ); document.write( "\"sqrt%2875%29=sqrt%2825%2A3%29=sqrt%2825%29%2Asqrt%283%29=5sqrt%283%29\"
\n" ); document.write( "and we do not like roots of any kind of root in denominators.
\n" ); document.write( "We could write a first step with roots in denominators and \"fix\" it later,but we can also fix it before, as in
\n" ); document.write( "\"sqrt%2875%2F2%29=sqrt%2875%2A2%2F4%29=sqrt%2875%2A2%29%2Fsqrt%284%29=sqrt%2875%2A2%29%2F2\"
\n" ); document.write( "Then,
\n" ); document.write( "
\n" ); document.write( "So \"sqrt%2875%2F2%29+%2B+root%283%2C2%2F4%29+=+5sqrt%286%29%2F2%2Broot%283%2C4%29%2F2\"
\n" ); document.write( "EXPLANATIONS ADDED:
\n" ); document.write( "2) (1/2)n^2 - n = 190 can be transformed into an equivalent equation by multiplying both sides times 2, and then subrracting 380 from both sides:
\n" ); document.write( "\"%281%2F2%29n%5E2+-+n+=+190\" --> \"2%28%281%2F2%29n%5E2+-+n%29+=+2%2A190\" --> \"2%28%281%2F2%29n%5E2%29+-+2%2An+=+2%2A190\" --> \"n%5E2+-+2n=380\" --> \"n%5E2-2n-380=0\"
\n" ); document.write( "If you needed to solve it, you could use the quadratic formula, or complete the square, like this:
\n" ); document.write( "\"n%5E2+-+2n=380\" --> \"n%5E2+-+2n%2B1=380%2B1\" (adding 1 to both sides)
\n" ); document.write( "Then writing the left side as the equivalent square, and adding as indicated on the right side:
\n" ); document.write( "\"%28n-1%29%5E2=381\" --> \"x=1+%2B-+sqrt%28381%29\"
\n" ); document.write( "3) (10x^2+5x)/5x=\"%2810x%5E2%2B5x%29%2F5x=2x%2B1\" As you divide or multiply a sum, you do that to every one of the terms added. If something priced 4 dollars and 50 cents is sold at half price , it will cost 2 dollars and 25 cents. You divide by two both parts of the price.
\n" ); document.write( "In math class we call that very logical fact \"the distribbutive property.\" It is the basis of the procedures for multiplication that we learn in elementary school. We multiply times a factor a large number by splitting that large number into a sum of smaller numbers, multiplying each samller number times the factor separately, and then adding. When you multiply 21 (20+1) times 4, you multiply the 1 to get 4 and the 2 tens (20) to get 8 tens (80), and then add up.
\n" ); document.write( "4) how to factor \"3x%5E2-15x\", the correct answer is 3x(x-5)
\n" ); document.write( "That is the distributive porperty again:
\n" ); document.write( "\"3x%28x-5%29=3x%2Ax-3x%2A5=3x%5E2-15\"
\n" ); document.write( "AND MORE EXPLANATIONS:
\n" ); document.write( "5) \"%284x-7%29%5E2\"= ?
\n" ); document.write( "The answer is not \"16x%5E2%2B49\".
\n" ); document.write( "That is just part of the answer, but you are missing something.
\n" ); document.write( "If you were to apply the distributive property, you would need to do it twice, like this:
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\n" ); document.write( "However, algebra students learn what the end result is for a square of a sum, so they do not have to mess with the intermediate steps.
\n" ); document.write( "Suppose you have the sum of two expressions, like \"4x\" and \"-7\", but we will call those two expressions A and B, for short. The square of A+B is
\n" ); document.write( "\"%28A%2BB%29%5E2=A%5E2%2B2AB%2BB%5E2\"
\n" ); document.write( "You would remember that easier if I draw it
\n" ); document.write( " The surface area of the big square is \"%28A%2BB%29%5E2=%28A%2BB%29%28A%2BB%29\"
\n" ); document.write( "It is made of 2 squares with areas \"A%5E2=A%2AA\" and \"B%5E2=B%2AB\", plus two rectangles, each with area \"A%2AB=AB\"
\n" ); document.write( "So the square of a sum (of two expressions) is the sum of the two squares plus the two rectangles.
\n" ); document.write( "So to calculate the square of \"4x\" plus \"-7\", we add the square of each, plus twice their product
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