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3 years ago

Expand the polynomial (x2 − y2)2 + (2xy)2 then simplify by combining like terms

Mathematics

2 answers:

rewona [7]3 years ago

8 0

Hello,

$(x^2-y^2)^2 + (2xy)^2=x^4-2x^2y^2+y^4+4x^2y^2\\

=x^4+2x^2y^2+y^4=(x^2+y^2)^2
$

Temka [501]3 years ago

4 0

Answer:

(x2 − y2)2 + (2xy)2

= x4 + y4 − 2x2y2 + 4x2y2 (apply (a − b)2 = a2 + b2 − 2ab to (x2 − y2) and square 2xy)

= x4 + y4 + 2x2y2 (simplify)

(x2 − y2)2 + 2(xy)2 = x4 + y4 + 2x2y2

This is answer is for plato.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Let

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substitute the values

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Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

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y----> the volume of the larger pyramid

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we have

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substitute

$\frac{7}{10}^{3}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{343}{1,000}$ -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

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we have

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

$(\frac{7}{10})^{3}=\frac{x}{12,000}$

$x=\frac{343}{1,000}(12,000)=4,116\ m^{3}$

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Answer:

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