9h^2 + 24h + 16 = (3h + 4)^2 ?

Question

How does it equal to (3h+4)^2 ?

Answer 1

9h² + 24h + 16 = (3h + 4)² Correct.
<><

Answer 2

Sorry, I should have explained this in a bit more detail in my earlier post.

You can verify this by multiplying out (3h + 4)^2 using the FOIL rule (First, Outside, Inside, Last):
(3h + 4)^2 = (3h + 4) (3h + 4)
= (3h).(3h) + (3h).(4) + (4).(3h) + (4).(4)
= 9h^2 + 12h + 12h + 16
= 9h^2 + 24h + 16

Now, as to how you can spot these factorisations - the main rule is to practise! However, there are a few specific types you should know:

(ax + b)^2 = a^2 x^2 + 2ab x + b^2. This was the kind we have above. Related is:
(ax - b)^2 = a^2 x^2 - 2ab x + b^2. (This is really the same, just replacing b with -b.)
If the coefficient of the square term and the constant term are both positive square numbers, take the square roots, multiply them together and double the result. If this matches the middle coefficient, you have one of these forms and the sign of the middle coefficient will tell you which one.

You should also know about the difference of perfect squares formula: a^2 - b^2 = (a - b) (a + b). For example, 9b^2 - 16 = (3b - 4) (3b + 4).

Answer 3

It's very easy. Just think at the meaning of "^2", e.g. the square power, it means multiplying a value by itself.

E.g.: ANYTHING^2 = ANYTHING * ANYTHING

So:

(3h + 4)^2 = (3h + 4)*(3h + 4)

Now, to multiply these two expressions, you must cross-multiply each term of each expression, as follows:

(3h + 4)*(3h + 4) = 3h*3h + 3h*4 + 4*3h + 4*4

so we found:

(3h + 4)^2 = 3h*3h + 3h*4 + 4*3h + 4*4

Now, observe that 3h*3h = 3*3*h*h = 9*h^2 = 9h^2
and: 3h*4 + 4*3h = 12h + 12h = 24h
and: 4*4 = 16

so we have that:
3h*3h + 3h*4 + 4*3h + 4*4 = 9h^2 + 24h + 16

Then we proved that:

(3h + 4)^2 = 9h^2 + 24h + 16

Answer 4

9h² + 24h + 16 = (3h + 4)²

9h² + 24h + 16 = 9h² + 24 + 16

9 h² + 24h + 16 - 9h² + 24 + 16 - 9h²

24h + 16 = 24h + 16

24h + 16 - 24j = 24h + 16 - 24h

16 = 16

16 - 16 - 16 - 16

0 = 0

- - - - - - - - - - -

9h² + 24h + 16 =

(3h + 4)(3h + 4).. .<=.This is the factor of 9h² + 24h + 16

- - - - - - - -s-

Answer 5

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

Answer 6

(a+b)^2 = a^2+2ab+b^2
And (a+b)^2 is also the same as (a+b)(a+b)

Therefore, 9h^2+24h+16= (3h+4)(3h+4)
=(3h+4)^2

Answer 7

Simplifying
9h2 + 24h + 16 = (3h + 4)(3h + 4)

Reorder the terms:
16 + 24h + 9h2 = (3h + 4)(3h + 4)

Reorder the terms:
16 + 24h + 9h2 = (4 + 3h)(3h + 4)

Reorder the terms:
16 + 24h + 9h2 = (4 + 3h)(4 + 3h)

Multiply (4 + 3h) * (4 + 3h)
16 + 24h + 9h2 = (4(4 + 3h) + 3h * (4 + 3h))
16 + 24h + 9h2 = ((4 * 4 + 3h * 4) + 3h * (4 + 3h))
16 + 24h + 9h2 = ((16 + 12h) + 3h * (4 + 3h))
16 + 24h + 9h2 = (16 + 12h + (4 * 3h + 3h * 3h))
16 + 24h + 9h2 = (16 + 12h + (12h + 9h2))

Combine like terms: 12h + 12h = 24h
16 + 24h + 9h2 = (16 + 24h + 9h2)

Add '-16' to each side of the equation.
16 + 24h + -16 + 9h2 = 16 + 24h + -16 + 9h2

Reorder the terms:
16 + -16 + 24h + 9h2 = 16 + 24h + -16 + 9h2

Combine like terms: 16 + -16 = 0
0 + 24h + 9h2 = 16 + 24h + -16 + 9h2
24h + 9h2 = 16 + 24h + -16 + 9h2

Reorder the terms:
24h + 9h2 = 16 + -16 + 24h + 9h2

Combine like terms: 16 + -16 = 0
24h + 9h2 = 0 + 24h + 9h2
24h + 9h2 = 24h + 9h2

Add '-24h' to each side of the equation.
24h + -24h + 9h2 = 24h + -24h + 9h2

Combine like terms: 24h + -24h = 0
0 + 9h2 = 24h + -24h + 9h2
9h2 = 24h + -24h + 9h2

Combine like terms: 24h + -24h = 0
9h2 = 0 + 9h2
9h2 = 9h2

Add '-9h2' to each side of the equation.
9h2 + -9h2 = 9h2 + -9h2

Combine like terms: 9h2 + -9h2 = 0
0 = 9h2 + -9h2

Combine like terms: 9h2 + -9h2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Answer 8

3h^2 is 9H
(3h x 4 is 12H ) x 2 is 24H
4x4 is 16

You need to expand the brackets becaause overall it is (3h + 4) x (3h + 4)

Answer 9

When you expand the RHS then you get the LHS.