Factor this please!(TRinomial)?

This is a perfect square: (3x+4)^2
If know how to factor, this should make sense. Otherwise, don't forget that the form of a perfect square is:
(ax)^2+2abx+b^2. Your trinomial is of that form.

(3x+4)(3x+4)

to check:
(do the FOIL or distribution method)

3x times 3x is 9x^2
3x times 4 is 12x
3x times 4 is 12x
4 times 4 is 16

9x^2+ 12x+12x+ 16 is equal to


9x^2+24x+16

9x^2 + 24x + 16
= 9x^2 + 12x + 12x + 16
= (9x^2 + 12x) + (12x + 16)
= 3x(3x + 4) + 4(3x + 4)
= (3x + 4)(3x + 4)
= (3x + 4)^2

(3x + 4)(3x + 4)-----is answer by inspection.

Could break down to :-
(3x)² + 8(3x) + 16
y² + 8y + 16
(y + 4)(y + 4)
(3x + 4)(3x + 4)

this trinomial is a perfect square trinomial"
the strategy on factoring perfect square is to get first the squar root
of the first term and the last term......9x^2+24x+16.......9x^2has a squareroot of "3x" while ...... 16 has" 4" and that's it place them in side a parenthesis........(3x+4)...and raise them to the second power
.........(3x+4)^2 this is the final ans. I hope this will help you.
you can do it !!

First off, notice that 9x^2 = (3x)^2
And 16 = 4^2

This gives you a good start point because if you think about it, 3x4 =12 and you have two of them which will give you 24x.

So, what you have here is a square: (3x + 4)^2

To solve/check your solution, expand:

(3x + 4) x (3x + 4) (now multiply each of the terms together)

= 9x^2 + 12x +12x + 16

= 9x^2 + 24x + 16

Method I:

we can express this trinomial as a perfect square.

9x^2 + 24x + 16
=(3x)^2 + 2.3x.4 + (4)^2
=(3x + 4)^2

Method II:
we can solve this trinomial by middle term factor

9x^2 + 24x + 16

Now LOOk: 9 x 16 = 144 ; 144 = 12 x 12 & 12 + 12 = 24

so we have,
9x^2 + (12 + 12)x + 16

= 9x^2 + 12x + 12x + 16

= 3x(3x+4) + 4(3x+4)

=(3x+4)(3x+4)

Hope this will surely help u :)

9x^2+24x+16 is a perfect square.
A perfect square follows the form (A^2 + 2AC + C^2)
Therefore, 9x^2+24x+16 = (3x)^2 + (2)(3x)(4) + (4)^2
9x^2+24x+16 = (3x + 4)^2.

9x^2+24x+16
= (3x)^2 + 2*(3x)(4) + (4)^2
= (3x + 4)^2.