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Tue 19 Jul, 2011 12:31 pm
Earlier in my Algebra book, it shows that (5y)^3 is equal to 5y*5y*5y/5*5*5*y*y*y, or 5^3*y^3. However, when learning about binomials, it says that (5+y)^2 isn't equal to 5^2+y^2, as I'd expect it to be, but it's 5^2+2(5)y+y^2. Where did that random 2(5)y come from? Is it the addition sign? What happened to the distributive property, simply distributing the exponent to all terms?
@JadElClemens,
Yes, it's the difference between raising a product (5 times y) to a power and a sum (5 plus y) being raised to a power. If you write it out as long multiplication (5+y)(5+y) you'll see that the result is y^2+10y+25.
@JadElClemens,
(5+y)^2=(5+y)(5+y)
Use the distributive rule to multiply
(5+y)(5+y)=5(5+y)+y(5+y)
5(5+y)+y(5+y)=(25+5y)+(5y+y^2)
Group terms
(25+5y)+(5y+y^2)=25+10y+y^2
putting into the 'books' form
25+10y+y^2 = 5^2+2*5y+y^2
The 2 isn't random--it comes from the distributive rule of multiplication.
Rap
@JadElClemens,
"Solution:Yes (5+y)²=(5+y)(5+y)
but if you multiply both (5+y)(5+y) then we will get the answer as =25+y²+10y
which is same as =5²+y²+2*5*y"
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