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3 years ago

Factor the expression 16a^2 - 81

Mathematics

1 answer:

Ray Of Light [21]3 years ago

8 0

Answer:

(4a - 9)(4a + 9)

Step-by-step explanation:

Every value in the equation has a square root

The square root of 16 is 4

The square root of a^2 is a

The square root of 81 is 9.

To factor you split the equation by the square roots. For 81, since the original value is negative, one of the roots must be negative so when you multiply it back out to the original, it stays the same.

You can check your answer this way too.

(4a -9)(4a + 9)

= 16a^2 + 36a - 36a - 81

= 16a^2 - 81

I hope this helps!

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4 years ago

The sum of the two areas of two circles is the 80x square meters. Find the length of a radius of each circle of them is twice as

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Answer:

$r = 4m$ --- small circle

$R =8m$ --- big circle

Step-by-step explanation:

Given

$Area = 80\pi\ m^2$ -- sum of areas

$R = 2r$

Required

The radius of the larger circle

Area is calculated as;

$Area = \pi r^2$

For the smaller circle, we have:

$A_1 = \pi r^2$

For the big, we have

$A_2 = \pi R^2$

The sum of both is:

$Area = A_1 + A_2$

$Area = \pi r^2 + \pi R^2$

Substitute: $R = 2r$

$Area = \pi r^2 + \pi (2r)^2$

$Area = \pi r^2 + \pi *4r^2$

Substitute $Area = 80\pi\ m^2$

$80\pi = \pi r^2 + \pi *4r^2$

Factorize

$80\pi = \pi[ r^2 + 4r^2]$

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$80 = 5r^2$

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3 0

3 years ago

Factor the expression 16a^2 - 81​

Factor the expression 16a^2 - 81