Question

simplify: (a+2b+c)^2 + (a+2b-c)^2​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• $\rm (a+2b+c)^2 + (a+2b-c)^2$

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$\red{\underline \bold{To \: Find:}}$

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• To simplify $\rm (a+2b+c)^2 + (a+2b-c)^2$

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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$\underline{\bold{\texttt{We know that ,}}}$

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$\sf \dag \ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\rm (a + 2b + c)^2 + (a + 2b -c)^2$

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It can be written as,

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$\sf \longmapsto (a + 2b + c)^2 + (a + 2b + (-c))^2$

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Now,

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$\sf \implies [a^2 + (2b)^2 + c^2 + 2a2b + 2c2b + 2ca] + [ a^2 + (2b)^2 + (-c)^2 + 2a2b + (-2c2b) + (-2ca)] </p><p></p><p>[tex] \:\:$

$\sf \implies [a^2 + 4b^2 + c^2 + 4ab + 4cb + 2ca] + [ a^2 + 4b^2 + c^2 + 4ab - 4cb - 2ca]$

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$\underline{\bold{\texttt{Simplifying further by addition of like terms}}}$

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↠$\sf [2a^2 + 8b^2 + 2c^2 + 8ab ]$

Answer 2

Answer :

›»› The expression is 2a² + 8ab + 8b² + 2c².

Given :

• (a + 2b + c)² + (a + 2b - c)².

To Solve :

• Simplify the expression.

Solution :

Let's start simplify the expression and understand the steps to get our final result of expression.

→ (a + 2b + c)² + (a + 2b - c)²

Expand an equation,

→ a² + 4ab + 2ac + 4b² + 4bc + c² + (a + 2b - c)²

Expand an equation,

→ a² + 4ab + 2ac + 4b² + 4bc + c² + a² + 4ab - 2ac + 4b² - 4bc + c²

Organize the similar terms,

→ (1 + 1)a² + (4 + 4)ab + (2 - 2)ac + (4 + 4)b² + (4 - 4)bc + (1 + 1)c²

Arrange the constant term,

→ 2a² + (4 + 4)ab + (2 - 2)ac + (4 + 4)b² + (4 - 4)bc + (1 + 1)c²

Arrange the constant term,

→ 2a² + 8ab + (2 - 2)ac + (4 + 4)b² + (4 - 4)bc + (1 + 1)c²

Organize the monomial expression andarrange the constant term,

→ 2a² + 8ab + 0ac + (4 + 4)b² + (4 - 4)bc + (1 + 1)c²

If we multiply a number by 0, it becomes 0,

→ 2a² + 8ab + 0 + (4 + 4)b² + (4 - 4)bc + (1 + 1)c²

Arrange the constant term,

→ 2a² + 8ab + 0 + 8b² + (4 - 4)bc + (1 + 1)c²

Organize the monomial expression and arrange the constant term,

→ 2a² + 8ab + 0 + 8b² + 0bc + (1 + 1)c²

If we multiply a number by 0, it becomes 0,

→ 2a² + 8ab + 0 + 8b² + 0 + (1 + 1)c²

Arrange the constant term,

→ 2a² + 8ab + 0 + 8b² + 0 + 2c²

0 does not change when we add or subtract,

→ 2a² + 8ab + 8b² + 2c²

Hence, the expression is 2a² + 8ab + 8b² + 2c².