please help me solve these problems! Thank you!
1. Simplify: (3p^5)(5p^2)+(7p^3)(2p^4)
2. Simplify: (6x^2-2xy+3y^2)-(4x^2-xy-y^2)
#1: 15p^7 - 14p^7 = ?
#2: just collect like exponents
(6-4)x^2 - (2+1)xy + (3+1)y^2
Sure! I'd be happy to help you solve these problems step by step.
1. To simplify the expression (3p^5)(5p^2) + (7p^3)(2p^4), we can use the properties of exponents.
First, we multiply the coefficients together: 3 * 5 = 15.
Next, we multiply the variables with the same base (p) by adding their exponents: p^5 * p^2 = p^(5+2) = p^7.
So, the first term simplifies to 15p^7.
For the second term, we again multiply the coefficients: 7 * 2 = 14.
Then, we multiply the variables with the same base (p) by adding their exponents: p^3 * p^4 = p^(3+4) = p^7.
So, the second term simplifies to 14p^7.
Finally, we add the simplified terms together: 15p^7 + 14p^7 = 29p^7.
Therefore, the simplified expression is 29p^7.
2. To simplify the expression (6x^2-2xy+3y^2)-(4x^2-xy-y^2), we can use the distributive property.
The expression can be rewritten as 6x^2 - 2xy + 3y^2 - 4x^2 + xy + y^2.
Next, we group the like terms together.
The terms with x^2 are 6x^2 and -4x^2, which simplifies to 6x^2 - 4x^2 = 2x^2.
The terms with xy are -2xy and xy, which simplifies to -2xy + xy = -xy.
The terms with y^2 are 3y^2 and y^2, which simplifies to 3y^2 + y^2 = 4y^2.
So, the simplified expression is 2x^2 - xy + 4y^2.
Therefore, (6x^2-2xy+3y^2)-(4x^2-xy-y^2) simplifies to 2x^2 - xy + 4y^2.
I hope this helps! Let me know if you have any other questions.