How to multiply (x³+2) (y²-3)
Answers
Answer:
Step-by-step explanation:
Let us multiply the given trinomial (x
3
−y
3
) by the binomial (x
2
+y
2
) as shown below:
(x
3
−y
3
)×(x
2
+3y
2
)=2x
4
+x
2
y
2
−15y
4
(x
3
−y
3
)(x
2
+y
2
)
=x
3
(x
2
+y
2
)−y
3
(x
2
+y
2
)
=(x
3
×x
2
)+(x
3
×y
2
)−(y
3
×x
2
)−(y
3
×y
2
)
=x
5
+x
3
y
2
−x
2
y
3
−y
5
Hence, (x
3
−y
3
)×(x
2
+y
2
)=x
5
+x
3
y
2
−x
2
y
3
−y
5
.
Step-by-step explanation:
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Step-by-step explanation:
First, solve for y…
y=2x
Substitute into other equation
x2−(2x)2=3
x2−(4x2)=3
x4x2−4x2=3
x4−4x2=3
x4−4=3x2
x4−3x2−4=0
Substitute. Let p=x2
Thus,
x4−3x2−4=0
becomes…
p2−3p−4=0
Simple Quadratic, factor..
(p−4)(p+1)=0
Substitute back in for p
(x2−4)(x2+1)=0
x2−4=0
x2=+4
x=2 or x=−2
Find y
xy=2
y=2x
y=2−2=−1 or y=22=1
Next, find x3+y3 and x3−y3.
Answer is -9, -7, 7, and 9.