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3 years ago

Factorize (X + 2 y)square - (2 x minus y) square

Mathematics

1 answer:

gulaghasi [49]3 years ago

3 0

Answer:

- (x - 3y)(3x + y)

Step-by-step explanation:

Given

(x + 2y)² - (2x - y)² ← expand both parenthesis using FOIL

= x² + 4xy + 4y² - (4x² - 4xy + y²) ← distribute

= x² + 4xy + 4y² - 4x² + 4xy - y² ← collect like terms

= - 3x² + 8xy + 3y² ← factor out - 1 from each term

= - 1(3x² - 8xy - 3y²) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the coefficient of the y² term which sum to give the coefficient of the xy- term.

product = 3 × - 3 = - 9 and sum = - 8

The factors are - 9 and + 1

Use these factors to split the xy- term

3x² - 9xy + xy - 3y² ( factor the first/second and third/fourth terms )

= 3x(x - 3y) + y(x - 3y) ← factor out (x - 3y) from each term

= (x - 3y)(3x + y)

Thus

(x + 2y)² - (2x - y)² = - (x - 3y)(3x + y)

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$y=64/x$

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see the draw in the attached figure N 1

case 2) For x=32 units

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$y=64/x$

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case 3) For x=16 units

substitute in the equation 1

$x*y=64$

$y=64/x$

$y=64/16$

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see the draw in the attached figure N 3

case 4) For x=30 units

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$x*y=64$

$y=64/x$

$y=64/30$

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case 5) For x=40 units

substitute in the equation 1

$x*y=64$

$y=64/x$

$y=64/40$

$y=1.60\ units$

the dimensions of the rectangle are 40 units x 1.60 units

see the draw in the attached figure N 5

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$x*y=64$

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$y=64/60$

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Factorize (X + 2 y)square - (2 x minus y) square​

Factorize (X + 2 y)square - (2 x minus y) square