Express 9x²-16y²-24xy as a square of a binomial.
Answers
Step-by-step explanation:
Note that:
9
x
2
=
(
3
x
)
2
24
x
y
=
2
(
3
x
)
(
4
y
)
16
y
2
=
(
4
y
)
2
So:
9
x
2
+
24
x
y
+
16
y
2
=
(
3
x
)
2
+
2
(
3
x
)
(
4
y
)
+
(
4
y
)
2
is in the form:
A
2
+
2
A
B
+
B
2
=
(
A
+
B
)
2
So putting
A
=
3
x
and
B
=
4
y
we have:
9
x
2
+
24
x
y
+
16
y
2
=
(
3
x
+
4
y
)
2
Answer:
= 9x2 – 24xy + 16y2
9x2 – 24xy + 16y2Given equation can be simplified as,
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2It is of the form a2 – 2ab + b2
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2It is of the form a2 – 2ab + b2Where a = 3x and b = 4y
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2It is of the form a2 – 2ab + b2Where a = 3x and b = 4y∴ using the identity (a – b)2 = a2 – 2ab + b2
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2It is of the form a2 – 2ab + b2Where a = 3x and b = 4y∴ using the identity (a – b)2 = a2 – 2ab + b2We get,
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2It is of the form a2 – 2ab + b2Where a = 3x and b = 4y∴ using the identity (a – b)2 = a2 – 2ab + b2We get,⇒ 9x2 – 24xy + 16y2 = (3x – 4y)2
9x2 – 24xy + 16y2Given equation can be simplified as,= (3x)2 – 2(3x)(4y) + (4y)2It is of the form a2 – 2ab + b2Where a = 3x and b = 4y∴ using the identity (a – b)2 = a2 – 2ab + b2We get,⇒ 9x2 – 24xy + 16y2 = (3x – 4y)29x2 – 24xy + 16y2 = (3x – 4y)2
Step-by-step explanation:
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