Question

Factorize x4+7x2y2+16y4
4 and 2 are squares
plz help or ill fail

Answer 1

Answer:

this by taking the HCF of the following numbers and keeping it in the front and the division of the HCF with each number in the brackets

Answer 2

Aɴꜱᴡᴇʀ

$({x}^{2} - 3 {y}^{2} )(x + 2y)(x - 2y)$

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Sᴛᴇᴘꜱ

${x}^{4} - 7 {x}^{2} {y}^{2} + 22 \times 3 {y}^{4}$

$({x}^{4} - 7 {x}^{2} \times {y}^{2} ) + 22 \times 3 {y}^{4}$

Step -1

Then we shall try to factor a multi variable polynomial

$( {x}^{4} - 7 {x}^{2} {y}^{2} ) + 22 \times 3 {y}^{4}$

factoring the given polynomial using trial and error

Step -2

Factorising

${x}^{2} - 3 {y}^{2}$

we can use the theory- The difference of 2 perfect squares can be factored into

(A+B)(A-B)

Step -3

Factorise

${x}^{2} - 4 {y}^{2}$

Check:4 is the square of 2

${x}^{2}$

is the square of

${x}^{1}$

similarly

${y}^{2}$

is the square of

${y}^{1}$

So factorisation is (x+2y)(x-2y)

Thus the final result

is

$({x}^{2} - 3 {y}^{2} ) (x + 2y)(x - 2y)$

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