Answer:
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
