want to know if this right simplify and show all work
-3x^2+4xy+7y^2+2(-3x^2+5xy+11y^2)
-3x^2+4xy+7y^2-6y^2+10xy+22y^2
-3x^2+14xy+45y^2
and
-6a-4a-2(100^2+3a)
-6a-4a^2+200+3a
3a-4a^2+200
in the second line of your solution, 2*(-3x^2) = -6x^2 not 6y^2. thus,
-3x^2 + 4xy + 7y^2 - 6x^2 + 10xy + 22y^2
-9x^2 + 14xy + 29y^2
..for the second problem, i think there are typos. please check the problem again. also, 100^2 is not equal to 200.
To simplify the expression -3x^2+4xy+7y^2+2(-3x^2+5xy+11y^2), we distribute the 2 to each term inside the parentheses:
-3x^2 + 4xy + 7y^2 + 2(-3x^2 + 5xy + 11y^2)
= -3x^2 + 4xy + 7y^2 - 6x^2 + 10xy + 22y^2
Now, combine like terms:
-3x^2 - 6x^2 + 4xy + 10xy + 7y^2 + 22y^2
= -9x^2 + 14xy + 29y^2
Thus, the simplified expression is -9x^2 + 14xy + 29y^2.
For the expression -6a-4a-2(100^2+3a), we first simplify the exponent 100^2, which equals 10,000. Then, we distribute the -2 to each term inside the parentheses:
-6a - 4a - 2(100^2 + 3a)
= -6a - 4a - 2(10000 + 3a)
Next, simplify the expression inside the parentheses:
-6a - 4a - 20000 - 6a
Now, combine like terms:
-6a - 4a - 20000 - 6a
= -16a - 20000
Thus, the simplified expression is -16a - 20000.
Finally, for the expression -6a-4a-2(100^2+3a), we simplify the exponent 100^2, which still equals 10,000. Then, we distribute the -2 to each term inside the parentheses:
-6a - 4a - 2(100^2 + 3a)
= -6a - 4a - 2(10000 + 3a)
Next, simplify the expression inside the parentheses:
-6a - 4a - 20000 - 6a
Now, combine like terms:
-6a - 4a - 20000 - 6a
= -16a - 20000
Thus, the simplified expression is -16a - 20000.
So the final result is 3a - 4a^2 + 200.