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3 years ago

Simplify (12a^{5}-6a-10a^{3})-(10a-2a^{5}-14a^{4})(12a 5 −6a−10a 3 )−(10a−2a 5 −14a 4 ) . Write the answer in standard form

Mathematics

1 answer:

Katen [24]3 years ago

6 0

Answer:

$(12a^{5}-6a-10a^{3})-(10a-2a^{5}-14a^{4}) = 14a^{5}+14a^{4}-10a^{3}-16a$

Step-by-step explanation:

Given

$(12a^{5}-6a-10a^{3})-(10a-2a^{5}-14a^{4})$

Required

Simplify

We have:

$(12a^{5}-6a-10a^{3})-(10a-2a^{5}-14a^{4})$

Open brackets

$12a^{5}-6a-10a^{3}-10a+2a^{5}+14a^{4}$

Collect like terms

$12a^{5}+2a^{5}+14a^{4}-10a^{3}-6a-10a$

$14a^{5}+14a^{4}-10a^{3}-16a$

Hence:

$(12a^{5}-6a-10a^{3})-(10a-2a^{5}-14a^{4}) = 14a^{5}+14a^{4}-10a^{3}-16a$

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4 years ago

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3 years ago

Rickey has been commissioned to paint a mural that is allowed to have an area of 50 square meters. To make the rectangle shape o

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Answer:

12.808 meter is the length should Rickey use for the mural.

Step-by-step explanation:

Area of the mural = A = $50 m^2$

Length of the mural = l

Width of the mural = w

l = 5 + 2w

Area of the rectangle = l × w

$A=(5+2w)\times w$

$50 m^2=5w+2w^2$

$2w^2+5w-50=0$

Solving above equation with the help of Completing squares method:

$(\sqrt{2}w)^2+2\times \sqrt{2}w\times \frac{5}{2\sqrt{2}}+(\frac{5}{2\sqrt{2}})^2-50=(\frac{5}{2\sqrt{2}})^2$

$(a+b)^2=a^2+b^2+2ab$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=(\frac{5}{2\sqrt{2}})^2+50$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=\frac{25}{8}+50$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})^2=\frac{425}{8}$

$(\sqrt{2}w+\frac{5}{2\sqrt{2}})=\pm\sqrt{\frac{425}{8}}$

w = 3.904 m (accept)

w = -6.404 m (reject)

l = (5 + 2w)m = 5 + 2 × (3.904) m= 12.808 m

12.808 meter is the length should Rickey use for the mural.

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3 years ago