The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + xz2 + yz – 24.
What is the value of x?
What is the value of y?
(4z^2 + 7z – 8)(–z + 3)
= -4z^3 + 12z^2 - 7z^2 + 21z + 8z - 24
= -4z^3 + 5z^2 + 29z - 24
matching this with –4z3 + xz2 + yz – 24
5z^2 = xz^2 ----> x = 5
29z = yz -----> y = 29
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To find the values of x and y, we need to expand the given expression and compare it with the given equation.
The product of (4z^2 + 7z – 8) and (–z + 3) can be found by using the distributive property:
(4z^2 + 7z – 8) * (–z + 3)
= (4z^2 + 7z – 8) * –z + (4z^2 + 7z – 8) * 3
= -4z^3 - 7z^2 + 8z + 12z^2 + 21z - 24
Comparing the expanded expression with the given equation:
-4z^3 - 7z^2 + 8z + 12z^2 + 21z - 24 = -4z^3 + xz^2 + yz - 24.
From this, we can equate the corresponding coefficients:
-7z^2 + 12z^2 = xz^2
8z + 21z = yz
Simplifying these equations:
5z^2 = xz^2 --- (1)
29z = yz --- (2)
To determine the value of x, we can divide both sides of equation (1) by z^2:
(5z^2) / (z^2) = (xz^2) / (z^2)
5 = x
Therefore, x = 5.
To determine the value of y, we can divide both sides of equation (2) by z:
(29z) / z = (yz) / z
29 = y
Therefore, y = 29.
Hence, the value of x is 5, and the value of y is 29.
To find the values of x and y, we need to expand the product of (4z^2 + 7z - 8) and (-z + 3) and then compare it to the given expression -4z^3 + xz^2 + yz - 24.
Let's start by distributing the terms from the first expression to the second expression:
(4z^2 + 7z - 8) * (-z + 3) = -4z^3 + 12z^2 -7z^2 + 21z + 8z - 24
Now let's compare this expanded expression to the given expression:
-4z^3 + 12z^2 - 7z^2 + 21z + 8z - 24 = -4z^3 + xz^2 + yz - 24
From the comparison, we can see that the x coefficient in the expanded expression is 12, and the y coefficient is 21.
Therefore, the value of x is 12 and the value of y is 21.