Question

Simplify: a(a+b^2+c)- b^2 (a+b+c)–c(a+b^2 )​

Answer 1

Answer:

a2+ab2+ac-ab2-b3-b2c-ac-b2c

a2-b3

Answer 2

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\large\boxed{\sf{a\left(a+b^2+c\right)-\:b^2\:\left(a+b+c\right)-c\left(a+b^2\right)}}$

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♣ ꜰᴏʀᴍᴜʟᴀ ᴜꜱᴇᴅ :

• $\sf{+\left(-a\right)=-a}$

• $\sf{a(b+c)=a b+a c}$

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♣ ᴀɴꜱᴡᴇʀ :

$\large\boxed{\sf{a\left(a+b^2+c\right)-\:b^2\:\left(a+b+c\right)-c\left(a+b^2\right)\bf{=a^2-b^3-2b^2c}}}$

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♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\sf{a\left(a+b^2+c\right)-b^2\left(a+b+c\right)-c\left(a+b^2\right)}$

$\bf{\text { Expand } a\left(a+b^{2}+c\right): a^{2}+a b^{2}+a c}$

$\sf{=a^2+ab^2+ac-b^2\left(a+b+c\right)-c\left(a+b^2\right)}$

$\bf{\text { Expand }-b^{2}(a+b+c):-a b^{2}-b^{3}-b^{2} c}$

$\sf{=a^2+ab^2+ac-ab^2-b^3-b^2c-c\left(a+b^2\right)}$

$\bf{\text { Expand }-c\left(a+b^{2}\right):-a c-b^{2} c}$

$\sf{=a^2+ab^2+ac-ab^2-b^3-b^2c-ac-b^2c}$

$\bf{\text { Simplify } a^{2}+a b^{2}+a c-a b^{2}-b^{3}-b^{2} c-a c-b^{2} c: a^{2}-b^{3}-2 b^{2} c}$

$\huge\boxed{\sf{=a^2-b^3-2b^2c}}$