plz help me
Identify the like terms
a) 2x+y+xy3+3y-x+3xy2
b) a2+b2+c2-3a2+2b2-5c2+2a+ b
c) a2b+ab2-1/2a +6b +abc+7ab2-7a2b+9a
b)
Answers
Answer:
GIVEN
\displaystyle \sf{ \frac{ {a}^{3} + 3 a{b}^{2} }{3 {a}^{2}b + {b}^{3} } = \: \frac{ {x}^{3} + 3 x{y}^{2} }{3 {x}^{2}y + {y}^{3} }}
3a
2
b+b
3
a
3
+3ab
2
=
3x
2
y+y
3
x
3
+3xy
2
TO PROVE
\displaystyle \sf{ \frac{x}{a} = \frac{y}{b} }
a
x
=
b
y
PROOF
\displaystyle \sf{ \frac{ {a}^{3} + 3 a{b}^{2} }{3 {a}^{2}b + {b}^{3} } = \: \frac{ {x}^{3} + 3 x{y}^{2} }{3 {x}^{2}y + {y}^{3} }}
3a
2
b+b
3
a
3
+3ab
2
=
3x
2
y+y
3
x
3
+3xy
2
By the Componendo - Dividendo rule we get
\displaystyle \sf{ \frac{ {a}^{3} + 3 a{b}^{2} + 3 {a}^{2}b + {b}^{3}}{ {a}^{3} + 3 a{b}^{2} - 3 {a}^{2}b - {b}^{3} } = \: \frac{ {x}^{3} + 3 x{y}^{2} + 3 {x}^{2}y + {y}^{3} }{{x}^{3} + 3 x{y}^{2} - 3 {x}^{2}y - {y}^{3} }}
a
3
+3ab
2
−3a
2
b−b
3
a
3
+3ab
2
+3a
2
b+b
3
=
x
3
+3xy
2
−3x
2
y−y
3
x
3
+3xy
2
+3x
2
y+y
3
\implies \: \displaystyle \sf{ \frac{ {(a + b)}^{3} }{ {(a - b)}^{3}} = \frac{ {(x + y)}^{3} }{ {(x - y)}^{3}} \: \: }⟹
(a−b)
3
(a+b)
3
=
(x−y)
3
(x+y)
3
\implies \: \displaystyle \sf{ \frac{ {(a + b)}^{} }{ {(a - b)}^{}} = \frac{ {(x + y)}^{} }{ {(x - y)}^{}} \: \: }⟹
(a−b)
(a+b)
=
(x−y)
(x+y)
Again by Componendo Dividendo Rule
\implies \: \displaystyle \sf{ \frac{ {(a + b + a + b)}^{} }{ {(a + b - a + b)}^{}} = \frac{ {(x + y + x - y)}^{} }{ {(x + y - x + y)}^{}} \: \: }⟹
(a+b−a+b)
(a+b+a+b)
=
(x+y−x+y)
(x+y+x−y)
\implies \: \displaystyle \sf{ \frac{2a}{2b} = \frac{2x}{2y} }⟹
2b
2a
=
2y
2x
\implies \: \displaystyle \sf{ \frac{a}{b} = \frac{x}{y} }⟹
b
a
=
y
x
\implies \: \displaystyle \sf{ \frac{x}{a} = \frac{y}{b} }⟹
a
x
=
b
y
SEE IN ATTACHMENT
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