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wlad13 [49]
2 years ago
14

Tomas learned that the product of the polynomials

rmula1" title="(a+b)(a^2-ab+b^2)" alt="(a+b)(a^2-ab+b^2)" align="absmiddle" class="latex-formula"> was a special pattern that would result in a sum of cubes, a^3+b^3.
His teacher put four products on the board and asked the class to identify which product would result in a sum of cubes if a=2x and b=y.
Mathematics
1 answer:
Liula [17]2 years ago
3 0

We are provided , Tomas learned <em><u>that a³ + b³ = (a + b ) ( a² - ab + b² )</u></em> , and his teacher writes four products on the board and we have to tell that which product suits the best if <em><u>a = 2x</u></em> and <em><u>b =</u></em><em><u> </u></em><em><u>y</u></em>

Now , putting a = 2x , b = y in the given formula we have :

{:\implies \quad \sf (2x)^{3}+(y)^{3}=(2x+y)\{(2x)^{2}-2\cdot x\cdot y+(y)^{2}\}}

{:\implies \quad \bf \therefore \quad \underline{\underline{(2x)^{3}+(y)^{3}=(2x+y)(4x^{2}-2xy+y^{2})}}}

Hence , The product <em>(2x+y) (4x²-</em><em>2</em><em>xy+y²)</em> would result in the sum of cubes of 2x & y :D

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\quad \huge \quad \quad \boxed{ \tt \:Answer }

\qquad \tt \rightarrow \:x = 16

____________________________________

\large \tt Solution  \: :

If two polygons are similar, their corresponding sides ratios will be equal to each other.

\qquad \tt \rightarrow \:  \cfrac{8}{16}  =  \cfrac{2x - 20}{24}

\qquad \tt \rightarrow \:  \cfrac{1}{2}  =  \cfrac{2x - 20}{24}

\qquad \tt \rightarrow \: 2x - 20 =  \cfrac{24}{2}

\qquad \tt \rightarrow \: 2x = 12 + 20

\qquad \tt \rightarrow \: 2x = 32

\qquad \tt \rightarrow \: x = 16

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

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