should i just expand the things raised to a power?? cause i know that i am not supposed to get any solutions from this problem cause the directions said just to factor it
Speaking from my great mathematical mathematics knowledge its already factored. You can expand the brackets if you want, but in a real world sense it is counter productive.
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Verified answer
(x+1)^3(4x-9)-(16x+9)(x+1)^2
=(x+1)^2[(x+1)(4x-9)-(16x+9)] (taking (x+1)^2 common)
=(x+1)^2[4x^2-9x+4x-9-16x-9]
=(x+1)^2[4x^2-21x-18]
=(x+1)^2[4x^2-24x+3x-18]
=(x+1)^2[4x(x-6)+3(x-6)]
=(x+1)^2 (x-6) (4x+3)
Notice that the first term has a factor of (x + 1)^3 while the second has a factor of (x + 1)^2.
Thus, we can factor out (x + 1)^2 to yield:
(4x - 9)(x + 1)^3 - (16x + 9)(x + 1)^2
=> (x + 1)^2 * [(4x - 9)(x + 1) - (16x + 9)]
= (x + 1)^2 * (4x^2 + 4x - 9x - 9 - 16x - 9)
= (x + 1)^2 * (4x^2 - 21x - 18)
= (x + 1)^2 * [(4x^2 - 24x) + (3x - 18)], by grouping
= (x + 1)^2 * [4x(x - 6) + 3(x - 6)]
= (4x + 3)(x - 6)(x + 1)^2.
I hope this helps!
Speaking from my great mathematical mathematics knowledge its already factored. You can expand the brackets if you want, but in a real world sense it is counter productive.
(x+1)^2[(x+1)(4x-9)-16x-9]
(x+1)^2[4x^2-9x+4x-9-16x-9]
(x+1)^2[4x^2-21x-18]
(x+1)^2[4x^2-24x+3x-18]
(x+1)^2[4x(x-6)+3(x-6)]
(x+1)^2(4x+3)(x-6)
There you go