a) 25a^2 - 16a^2 b^2
b) x^2 - (a+b)^2
c) 9(x-y)^2 - z^2
d) 16x^4 - 81y^4
e) 25a^2 - 16a^2 b^2
14/22 X 3/9
Adam earned 60 points in a video game. He lost 50 points earned 67 points,then lost 20 more points. Write and evaluate an expression yo find his final score in the video game
a) To simplify the expression 25a^2 - 16a^2 b^2, we can factor out the common factor of a^2. This gives us:
25a^2 - 16a^2 b^2 = a^2(25 - 16b^2)
b) To simplify the expression x^2 - (a+b)^2, we can start by expanding the squared term using the formula (a+b)^2 = a^2 + 2ab + b^2. So we have:
x^2 - (a+b)^2 = x^2 - (a^2 + 2ab + b^2)
= x^2 - a^2 - 2ab - b^2
c) To simplify the expression 9(x-y)^2 - z^2, we can use the distributive property to expand the squared term:
9(x-y)^2 - z^2 = 9(x^2 - 2xy + y^2) - z^2
= 9x^2 - 18xy + 9y^2 - z^2
d) To simplify the expression 16x^4 - 81y^4, we can recognize that this is a difference of squares. We can rewrite it as:
16x^4 - 81y^4 = (4x^2)^2 - (9y^2)^2
= (4x^2 - 9y^2)(4x^2 + 9y^2)
e) This expression was provided earlier, so to simplify it, we can follow the same steps as in part (a):
25a^2 - 16a^2 b^2 = a^2(25 - 16b^2)
These are the simplified forms of the given expressions.