Which polynomial is paired to its factored form? 36x2 + 18x + 9 and (6x + 3)2 49x2 + 56x − 16 and (7x − 4)2 729x3 − 405x2 + 225x − 125 and (9x − 5)3 64x3 + 384x2 + 768x + 512 and (4x + 8)3

64x^3 + 384x^2 + 768x + 512 and (4x + 8)^3

Step-by-step explanation:

Here, we want to check which of the polynomials is placed with its factored form.

What we only need to do here is to find the product of the factored form and see if it gives us the polynomial ;

36x^2 + 18x + 9

(6x + 3)^2

= 6x(6x + 3) + 3(6x + 3)

= 36x^2 + 18x + 18x + 9

= 36x^2 + 36x + 9

This is wrong

49x^2 + 56x -16

(7x-4)^2

= 7x(7x-4) -4(7x -4)

= 49x^2 -28x -28x + 16

49x^2 -56x + 16

This is wrong also

729x^3 -405x^2 + 225x -125

(9x -5)^3

= (9x-5)(9x-5)^2

= (9x-5)(9x(9x-5) -5(9x-5))

= (9x-5)(81x^2 -45x -45x + 25))

= (9x-5)(81x^2 -90x + 25)

= 9x(81x^2 -90x + 25) -5(81x^2 -90x + 25)

= 729x^3 -810x^2 + 225x - 405x^2 + 450x -125

= 729x^3 -1215x^2 + 675x -125

This is also wrong

That makes the last number a possible answer; let’s check

(4x + 8)^3 = (4x + 8)(4x + 8)^2

= (4x + 8)(4x + 8)^2

= (4x + 8)(4x(4x + 8) + 8(4x + 8))

= 4x + 8(16x^2 + 32x + 32x + 64)

= (4x + 8)(16x^2 + 64x + 64)

= 4x(16x^2 + 64x + 64) + 8(16x^2 + 64x + 64)

= 64x^3 + 256x^2 + 256x + 128x^2 + 512x + 256

= 64x^3 + 256x^2 + 128x^2 + 512x + 256x + 256

= 64x^3 + 384x^2 + 768x + 256

square root

step-by-step explanation: