Question

subtract the sum of 12ab - 10b² - 18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a²​

Answer 1

$\bigstar \: {\underline{\mathfrak{Answer \:-}}}$

• -20ab + 3b² + 3a².

$\bigstar \:{\underline{\mathfrak{What \: to \: do \: -}}}$

• Subtract the sum of 12ab - 10b² - 18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a².

$\bigstar \:{\underline{\mathfrak{Step\!-\!by\!-\!step \: explanation \: -}}}$

• To solve this sum, let's first find the sum of 12ab - 10b² - 18a² and 9ab + 12b² + 14a², then the sum of ab + 2b² and 3b² - a² and finally subtract to get our answer!

$\bigstar$ Sum of 12ab - 10b² - 18a² and 9ab + 12b² + 14a² :-

$\hookrightarrow$ (12ab - 10b² - 18a²) + (9ab + 12b² + 14a²)

$\hookrightarrow$ 12ab - 10b² - 18a² + 9ab + 12b² + 14a²

$\hookrightarrow$ 12ab + 9ab - 10b² + 12b² - 18a² + 14a²

$\hookrightarrow$ 21ab + 2b² - 4a²

$\bigstar$ Sum of ab + 2b² and 3b² - a² :-

$\hookrightarrow$ (ab + 2b²) + (3b² - a²)

$\hookrightarrow$ ab + 2b² + 3b² - a²

$\hookrightarrow$ ab + 5b² - a²

$\bigstar$ Difference between 21ab + 2b² - 4a² and ab + 5b² - a² :-

$\hookrightarrow$ (ab + 5b² - a²) - (21ab + 2b² - 4a²)

$\hookrightarrow$ ab + 5b² - a² - 21ab - 2b² + 4a²

$\hookrightarrow$ab - 21ab + 5b² - 2b² - a² + 4a²

$\hookrightarrow$ - 20ab + 3b² + 3a²

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Note - While subtracting two or more algebraic expressions, we change the sign of each term to be subtracted and then add. This is what we did here to get our answer.

Hence -

• Our answer is -20ab + 3b² + 3a².

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Answer 2

Question:-

subtract the sum of 12ab - 10b² - 18a² and 9ab + 12b² + 14a² from the sum of ab + 2b² and 3b² - a².

Solution:-

Sum of 12ab - 10b² - 18a² and 9ab + 12b² + 14a²

= 12ab - 10b² - 18a² + 9ab + 12b² + 14a² ---->(1)

Sum of ab + 2b² and 3b² - a²

= ab + 2b² + 3b² - a² ---->(2)

Subtracting (1) from Equation (2)

⇒ - a² + 5b² + ab - ( - 4a² + 2b² + 21ab )

⇒ a² ( - 1 + 4 ) + b² ( 5 - 2 ) + ab ( 1 - 21 )

⇒ 3a² + 3b² - 20ab

Answer:-

$\sf \small \mathfrak \red{Hence,the \: answer = 3a {}^{2} + 3b {}^{2} - 2ab.⚘}$