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. (3p^5*5p^2) + (7p^3*2p^4) =
15p^7 + 14p^7 = 29p^7
2. (6x^2-2xy+3y^2)-(4x^2-xy-y^2) =
6x^2-2xy+3y^2 -4x^2+xy+y^2 =
2x^2 - xy + 4y^2
Of course! I'd be happy to help you solve these problems.
1. Simplify: (3p^5)(5p^2) + (7p^3)(2p^4)
To simplify this expression, you can use the product of powers property, which states that when you multiply two terms with the same base, you add their exponents.
Let's simplify each term separately first:
(3p^5)(5p^2) = 3 * 5 * p^5 * p^2 = 15p^(5+2) = 15p^7
(7p^3)(2p^4) = 7 * 2 * p^3 * p^4 = 14p^(3+4) = 14p^7
Now, we can combine these simplified terms:
15p^7 + 14p^7 = 29p^7
So the simplified expression is 29p^7.
2. Simplify: (6x^2-2xy+3y^2)-(4x^2-xy-y^2)
To simplify this expression, you need to distribute the negative sign to each term inside the parentheses using the distributive property.
In the first set of parentheses: (6x^2 - 2xy + 3y^2)
In the second set of parentheses: (4x^2 - xy - y^2)
Now distribute the negative sign to each term in the second set of parentheses:
-(4x^2 - xy - y^2) = -4x^2 + xy + y^2
Now, you can combine like terms by subtracting or adding coefficients:
6x^2 - 2xy + 3y^2 - 4x^2 + xy + y^2
Combine the terms with the same variables:
(6x^2 - 4x^2) + (-2xy + xy) + (3y^2 + y^2) = 2x^2 - xy + 4y^2
So the simplified expression is 2x^2 - xy + 4y^2.
I hope this helps! Let me know if you have any further questions.