Question

answer with steps pls​

Answer 1

Step-by-step explanation:

$16 {x}^{2} + 40x + 25$

Splitting the middle term method:

For an equation ax² + bx + c,

we need to split b into two terms such that sum of two terms is b and product of two terms is ac

Here, a = 16, b = 40 & c = 25

we need to find two terms x and y such that

x + y = 40 & xy = 25*16 = 400

we can see that x = 20 & y = 20 solves both the equations

Therefore,

$16 {x}^{2} + 40x + 25$

$= > 16 {x}^{2} + 20x + 20x + 25$

$= > 4x(4x + 5) + 5(4x + 5)$

$= > (4x + 5)(4x + 5)$

Important notes:

When you cannot guess the numbers, follow the following method

Consider two numbers

$(\frac{sum}{2} + x ) \: and \: ( \frac{sum}{2} - x)$

such that the product is as required

Here, sum = 40 & product = 400

Therefore, the numbers will be

$( \frac{40}{2} + x) \: and \: ( \frac{40}{2} - x)$

$= > (20 + x) \: and \: (20 - x)$

Product should be 400

$= > (20 + x)(20 - x) = 400$

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

=>

$= > {20}^{2} - {x}^{2} = 400$

$= > 400 - {x}^{2} = 400$

$= > {x}^{2} = 0$

$= > x = 0$

Therefore, the numbers will be 20 & 20

Hope this helps!

Answer 2

Answer:

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Step-by-step explanation:

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