Question

Evaluate:-

1) (a² + 5) (a² - 3)
2) (4 - ab) (8 + ab)​

Answer 1

$(a^2 + 5)(a^2-3)\\\\(x+a)(x+b) = x^2 + (a+b)x + ab\\\\here \\\\x=a\\\\a = 5\\\\b=-3\\\\(a^2 + 5)(a^2-3) = (a^2)^2 + (5 +(-3)) a^2 + (5* - 3)\\\\(a^2 + 5)(a^2-3) = a^4 + 2a^2 - 15$

$2)\\\\(4 - ab) (8 + ab)\\\\4(8 + ab) = 32 + 4 ab \\\\-ab(8 + ab) = -8ab \\\\32 + 4ab - 8ab = 32 - 4ab\\\\= 32-4ab$

hope it helps !!

Answer 2

$\sf{\red{\boxed{\bold{Solution\: 1}}}}$

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$\sf:\implies \: {\bold{ ( a^2 + 5)( a^2 - 3) }}$

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$\sf:\implies \: {\bold{ a^2( a^2 - 3) + 5( a^2 -3)}}$

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$\sf:\implies \: {\bold{ a^3 -3a^2 + 5a^2 -3}}$

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$\sf:\implies \: {\bold{ a^3 + 2a^2 - 3}}$

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_________________________

$\sf{\red{\boxed{\bold{Solution\: 2}}}}$

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$\sf:\implies \: {\bold{ (4-ab)( 8 +ab) }}$

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$\sf:\implies \: {\bold{ 4 ( 8 +ab) - ab ( 8 + ab)}}$

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$\sf:\implies \: {\bold{ 32 + 4ab - 8ab + a^2b^2}}$

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$\sf:\implies \: {\bold{ 32 - 4ab + a^2b^2}}$