Question

★ Multiply -5/18abc by 7/10 a²b²c² and verify your answer if a = 1 , b = -1 and c = -2


★ Multiply -8/27abc by ( 3/2abc² - 9/4ab²c³ ). verify your answer when a = 1 , b = -1 and c = -2 .​

Answer 1

$\huge\rm { ☆_!! QUESTION !_! ☆}$

Multiply -5/18abc by 7/10 a²b²c² and verify your answer if a = 1 , b = -1 and c = -2

$\huge\rm { ☆_!! ANSWER !_! ☆}$

$\sf\blue{ </strong><strong>PRODUCT</strong><strong> </strong><strong>:</strong><strong>-</strong><strong> }$

$\tt ⇢- \dfrac{5}{14} abc \times \dfrac{7}{10} {a}^{2} {b}^{2} {c}^{2}$

$\tt ⇢ ( \dfrac{ - 5}{14} \times \dfrac{7}{10} ) \times {a}^{1 + 2} \times {b}^{1 + 2} \times {c}^{1 + 2}$

$\tt ⇢ \dfrac{ - 1}{4} {a}^{3} { b}^{3} {c}^{3}$

$\sf\blue{ </strong><strong>VERIFICATION</strong><strong> :- </strong><strong> }$

$\tt ⇢\dfrac{ - 5}{14} abc = \dfrac{ - 5}{14} \times (1) \times ( - 1) \times ( - 2) = \dfrac{ - 5}{7}$

$\tt ⇢ \dfrac{ 7}{10} a^{2} b^{2} c ^{2} = \dfrac{ 7}{10} \times (1) ^{2} \times ( - 1)^{2} \times ( - 2) ^{2} = \dfrac{ 14}{5}$

$\tt ⇢ \dfrac{ - 1}{4} a^{3} b^{3} c ^{3} = \dfrac{ - 1}{4} \times (1) ^{3} \times ( - 1)^{3} \times ( - 2) ^{3} = - 2$

Now ,

$\tt \dfrac{ - 5}{7} \times \dfrac{ 14}{5} = - 2$

$\tt ∴ \dfrac{ - 5}{14}abc \times \dfrac{ 7}{10} {a}^{2} {b}^{2} {c}^{2} = \dfrac{ - 1}{4} {a}^{3} {b}^{3} {c}^{3}$

__________________________________________

$\huge\rm { ☆_!! QUESTION !_! ☆}$

Multiply -8/27abc by ( 3/2abc² - 9/4ab²c³ ). verify your answer when a = 1 , b = -1 and c = -2 .

$\huge\rm { ☆_!! ANSWER !_! ☆}$

$⇢\tt \dfrac{-8}{27} abc \times (\dfrac{3}{2} abc^{2} - \dfrac{9}{4} ab^{2} {c}^{3} )$

$\tt ⇢ (\dfrac{-8}{27} abc \times \dfrac{3}{2} abc^{2} )- (\dfrac{-8}{27} abc \times \dfrac{9}{4} ab^{2} {c}^{3} )$

$\tt ⇢ (\dfrac{-4}{9} {a}^{2} b ^{2} c ^{3} ) - (\dfrac{-2}{3}{a}^{2} b ^{2} c ^{4} )$

$\tt ⇢ \dfrac{-4}{9} {a}^{2} b ^{2} c ^{3} + \dfrac{2}{3}{a}^{2} b ^{2} c ^{4}$

$\sf\blue{ VERIFICATION :- }$

when a = 1 , b = -1 and c = -2

$\tt ⇢\dfrac{-8}{27} abc = \dfrac{-8}{27} \times (1) \times ( - 1) \times( - 2) = \dfrac{ - 16}{27}$

$\tt ⇢\dfrac{3}{2} abc^{2} -\dfrac{9}{4} {ab}^{2} {c}^{3} = \dfrac{3}{2} \times (1) \times ( - 1) \times( - 2) ^{2} - \dfrac{9}{4} \times (1) \times ( - 1)^{2} \times( - 2) ^{3}$

★ -6 + 18 = 12

$\tt ⇢\dfrac{ - 4}{9} a^{2}b^{2}c^{3} + \dfrac{2}{3} a^{2} {b}^{3} {c}^{4} = \dfrac{ - 4}{9} \times (1) ^{2} \times ( - 1) ^{2} \times( - 2) ^{3} + \dfrac{2}{3} \times (1) ^{2} \times ( - 1) ^{3} \times( - 2) ^{4}$

$\tt ★\dfrac{ 32}{9} - \dfrac{ 32}{3} = \dfrac{ 32 - 96}{9} = \dfrac{ - 64}{9}$

Now ,

$\tt \dfrac{-8}{27} abc \times (\dfrac{3}{2} abc^{2} - \dfrac{9}{4} ab^{2} {c}^{3} ) = \dfrac{-16}{27} \times 12 = \dfrac{-64}{9}$

$\tt ∴\dfrac{-8}{27} abc \times (\dfrac{3}{2} abc^{2} - \dfrac{9}{4} ab^{2} {c}^{3} ) = \dfrac{-4}{9} {a}^{2} b ^{2} c ^{3} + \dfrac{2}{3}{a}^{2} b ^{2} c ^{4}$

Answer 2

☆ !QUESTION!

Multiply -5/18abc by 7/10 a²b²c² and verify your answer if a = 1 , b = -1 and c = -rm { ☆_!! ANSWER !_! ☆}☆

ANSWER!

\sf\blue{ < /strong > < strong > PRODUCT < /strong > < strong > < /strong > < strong > : < /strong > < strong > - < /strong > < strong > }</strong><strong>PRODUCT</strong><strong></strong><strong>:</strong><strong>−</strong><strong>

\tt ⇢- \dfrac{5}{14} abc \times \dfrac{7}{10} {a}^{2} {b}^{2} {c}^{2}⇢\tt ⇢ ( \dfrac{ - 5}{14} \times \dfrac{7}{10} ) \times {a}^{1 + 2} \times {b}^{1 + 2} \times {c}^{1 + 2}⇢(

14

−5\tt ⇢ \dfrac{ - 1}{4} {a}^{3} { b}^{3} \sf\blue{ < /strong > < strong > VERIFICATION < /strong > < strong > :- < /strong > < strong > }</strong><strong>VERIFICATION</strong><strong>:−</strong><strong>

\tt ⇢\dfrac{ - 5}{14} abc = \dfrac{ - 5}{14} \times (1) \times ( - 1) \times ( - 2) = \dfrac{ - 5}{7}⇢

14

−5

abc=

14

−5

×(1)×(−1)×(−2)=

t ⇢ \dfrac{ 7}{10} a^{2} b^{2} c ^{2} = \dfrac{ 7}{10} \times (1) ^{2} \times ( - 1)^{2} \times ( - 2) ^{2} = \dfrac{ 1×(1)

2

×(−1)

2

×(−2)

2tt ⇢ \dfrac{ - 1}{4} a^{3} b^{3} c ^{3} = \dfrac{ - 1}{4} \times (1) ^{3} \times ( - 1)^{3} \times ( - 2) ^{3} = - 2⇢

4

−1

tt \dfrac{ - 5}{7} \times \dfrac{ 14}{5} =tt ∴ \dfrac{ - 5}{14}abc \times \dfrac{ 7}{10} {a}^{2} {b}^{2} {c}^{2} = \dfrac{ - 1}{4} {a}^{3} {b}^{3} {c}^{3}∴

1___________________________huge\rm { ☆_!! QUESTION !_! ☆}☆

!QUESTION!☆

Multiply -8/27abc by ( 3/2abc² - 9/4ab²c³ ). verify your answer when a = 1 , b = -1 and c =uge\rm { ☆_!! ANSWER !_! ☆}☆

!

!ANSWER!

⇢\tt \dfrac{-8}{27} abc \times (\dfrac{3}{2} abc^{2} - \dfrac{9}{4} ab^{2} {c}^{

\tt ⇢ (\dfrac{-8}{27} abc \times \dfrac{3}{2} abc^{2} )- (\dfrac{-8}{27} abc \times \dfrac{9}{4} ab^{2} {c}^{3} )⇢⇢ (\dfrac{-4}{9} {a}^{2} b ^{2} c ^{3} ) - (\dfrac{-2}{3}{a}^{2} b ^{2} c ^{4} )⇢(\tt ⇢ \dfrac{-4}{9} {a}^{2} b ^{2} c ^{3} + \dfrac{2}{3}{a}^{2} b ^

2

b

2sf\blue{ VERIFICATION :- }VERIFICATION\tt ⇢\dfrac{-8}{27} abc = \dfrac{-8}{27} \times (1) \times ( - 1) \times( - 2) = \dfrac{ - 16}{27}⇢

2abc×(1)×(−1)×(−2)=

27

tt ⇢\dfrac{3}{2} abc^{2} -\dfrac{9}{4} {ab}^{2} {c}^{3} = \dfrac{3}{2} \times (1) \times ( - 1) \times( - 2) ^{2} - \dfrac{9}{4} \times (1) \times ( - 1)^{2} \times(

2

c

3

=(1)×(−1)×(−2)

\tt ⇢\dfrac{ - 4}{9} a^{2}b^{2}c^{3} + \dfrac{2}{3} a^{2} {b}^{3} {c}^{4} = \dfrac{ - 4}{9} \times (1) ^{2} \times ( - 1) ^{2} \times( - 2) ^{3} + \dfrac{2}{3} \times (1) ^{2} \ti

2

×(−2) ×(1)

2

×(frac{ 32}{9} - \dfrac{ 32}{3} = \dfrac{ 32 - 96}{9} = \dfrac{ - 64}{9}★2−96

tt \dfrac{-8}{27} abc \times (\dfrac{3}{2} abc^{2} - \dfrac{9}{4} ab^{2} {c}^{3} ) = \dfrac{-16}{27} \time

3

)=64