Find the value of the polynomial:
7x^2y−2xy^2−6x^2y+3xy^2−xy+8 for x=−2, y=4
The answer is 0 based on what I got i dont if it is right
Its 0!
Hey there! This question has stumped me too. I think you might be surprised that the answer is 0! Wow!
Well, well, let's put on our math hat and calculate this colorful polynomial!
When we substitute x = -2 and y = 4 into the polynomial, we get:
7(-2)^2(4) - 2(-2)(4)^2 - 6(-2)^2(4) + 3(-2)(4)^2 - (-2)(4) + 8
Simplify this down, and we have:
7(4)(4) - 2(-2)(16) - 6(4)(4) + 3(-2)(16) + 8(2) + 8
Now, let's do some math magic:
112 - (-64) - 96 - (-96) + 16 + 8
Simplifying further:
112 + 64 - 96 + 96 + 16 + 8
Drumroll, please:
200!
So the value of the polynomial with x = -2 and y = 4 is 200. Ta-da!
To find the value of the polynomial 7x^2y - 2xy^2 - 6x^2y + 3xy^2 - xy + 8 for x = -2 and y = 4, we need to substitute these values into the polynomial expression and simplify.
Let's go step by step:
Step 1: Substitute the given values of x and y into the polynomial expression:
7(-2)^2(4) - 2(-2)(4)^2 - 6(-2)^2(4) + 3(-2)(4)^2 - (-2)(4) + 8
Step 2: Simplify each term:
7(4)(4) - 2(-2)(16) - 6(4)(4) + 3(-2)(16) - (-2)(4) + 8
112 + 64 + 96 - 96 + 8 + 8
Step 3: Combine like terms:
112 + 64 + 96 - 96 + 8 + 8
(112 + 8) + (64 + 96 - 96) + 8
120 + 64 + 8
192
So, the value of the polynomial 7x^2y - 2xy^2 - 6x^2y + 3xy^2 - xy + 8 when x = -2 and y = 4 is 192.
just plug in the numbers.
7(-2)^2*4−2(-2)*4^2−6(-2)^2*4+3(-2)*4^2−(-2)*4+8
Do it by hand, or plug it into any online calculator.
Or, simplify a bit first, and evaluate
x^2y + xy^2 - xy + 8 = xy(x+y-1) + 8
that might be a bit easier.