Can you please help me with this factorizing problem!!!!?

Hi,

Here are some examples of problems like yours before we get to your problem.


Suppose you had 4x² - 81
This is the difference of perfect squares. 4x² is really (2x) squared. 81 is 9². So both factors start with 2x and both end with 9. One binomial has a "-" and the other has a "+".

The factors are (2x - 9)(2x + 9).

Suppose you had 16a² - 49
This is the difference of perfect squares. 16a² is really (4a) squared. 49 is 7². So both factors start with 4a and both end with 7. One binomial has a "-" and the other has a "+". The order does not matter.

The factors are (4a + 7)(4a - 7).

Suppose you had 18x² - 50
18 and 50 are not perfect squares because no number times itself equals either 18 or 50. The problem is that we did not look first for a GCF! This time both terms are divisible by 2. If we divide that out first, we get:
2(9x² - 25) Now we have a difference of perfect squares!
Keep the GCF of 2 out front. The parentheses has a difference of perfect squares. 9x² is really (3x) squared. 25 is 5². So both factors start with 3x and both end with 5. One binomial has a "-" and the other has a "+".

The factors are 2(3x - 5)(3x + 5).

Suppose you had 16x^4 - 81
This is the difference of perfect squares. 16x^4 is really (4x²) squared. 81 is 9². So both factors start with 4x² and both end with 9. One binomial has a "-" and the other has a "+". The order does not matter.

(4x² + 9)(4x² - 9) This is correct so far, but it is not done this time. Notice that with x² in terms with 4 and 9, that they are perfect squares again, so the factor that is the DIFFERENCE of perfect squares can factor again. (The sum of perfect squares can not factor.) So (4x² - 9) factors again into:

(4x² + 9)(4x² - 9)
(4x² + 9)(2x - 3)(2x + 3) <== This is the answer in factored form.

Now, your problem, 16b² - 144

While 16b² - 144 could factor into (4b - 12)(4b + 12), that is not completely factored because the GCF was not divided out first. Instead, divide out a GCF of 16 first.

16b² - 144 =

16(b² - 9) =

Keep the GCF of 16 out front. The parentheses has a difference of perfect squares. b² is really (b) squared. 9 is 3². So both factors start with b and both end with 3. One binomial has a "-" and the other has a "+".

16(b - 3)(b + 3) <==ANSWER

I hope that helps!! :-)

answer: (-x - 2) * (4y - 3) = 3x -8y -4xy +6 yet HOW do you get it? easily, the least complicated way is to apply between the numerous factoring calculators you discover on the information superhighway. in simple terms Google on "factoring calculator," and you will discover a raft of them, quite often loose. attempt some. %. one you like. yet, in case you would be classic, listed below are some clues for fixing this via "inspection." it quite is a huge term. It ability shop guessing till you get it. right here, you notice the plus six on the tip. the only thank you to get a plus there is to have the indicators alike in the two binomials. they could the two be the two pluses, or the two minuses. then you definately see there are a pair minus words in what you're attempting to element, which ability there is a minimum of one minus sign someplace in the element pair. and you already know already the indicators are alike. So,that proves that the indicators in the two your binomials would be detrimental, for the reason which you may desire to not get a detrimental in the product AND an excellent very final quantity any opposite direction. so far, you have on your psychological photograph something like this: (aaa - bbb) * (ccc - ddd) Now, bbb situations ddd could equivalent 6. do not waste time with a million and 6, because of the fact the three in front of the x tells you 6 could be impossible; ddd could be 3, and aaa could be -x as a manner to make the constructive 3x in the expression you're factoring. So, retaining up which contain your truthfully marvelous good judgment: (-x - 2) * (ccc - 3) it quite is downhill from right here. ccc could be some style of y's that make -8y whilst stronger via -2. Duhhhh... permit's attempt 4y. Bingo! it incredibly works. Checking it out: (-x - 2) * (4y - 3) = 3x -8y -4xy +6 ok, flow make popcorn.

to check the factorized problem, we multiply your final answer which is
(4b-12)(4b+12)

we use the foil we multipling trinomial.
=16b^2-48b+48b-144
=16b^2-144

hope that helps.

Simplifying
16b2 + -144
Mine =

Reorder the terms:
-144 + 16b2

Factor out the Greatest Common Factor (GCF), '16'.
16(-9 + b2)

Factor a difference between two squares.
16((3 + b)(-3 + b)

)Final result:16(3 + b)(-3 + b)

(4b-12)(4b+12) You should times everything by everything
(4bx4b/ 4bx12/ -12x4b/ -12x12)
4bx4b= 16b^2 (4x4=16, bxb=b^2)
middle pretty self explanitory
-12x12=-144 (minus x positive always= minus)

So you get 16b^2+48b-48b-144
The 38b's cancel each other out and you're left with 16b^2-144

Multiply out the brackets. use the 'crab's claw' method:-

Start with the left bracket, and multiply each term by the terms in the right bracket:-

(4b * 4b) + (4b * 12) + (-12 * 4b) + (-12 *12)

If you draw a curved line from 4b to 4b (4b*4b), and do that for each multiplication, you will get a 'crab's claw' - this sort of helps you remember the order of multiplication when you 'expand' two brackets like this.

Finishing off the sum above:-

16b² + 48b - 48b - 144

The 48b terms cancel each other out, giving:-

16b² - 144 as required.

***EDIT:- Karan Harshit, do you make a habit of copying other user's answers???????

(4b-12)(4b+12)
=(4bx4b) + (-12x4b) + (12x4b) + (12x12) [expand brackets]
=16b^2 + -48b + 48b + 144 [-48b and 48b cancel out]
=16b^2 +144

Hi Tasha,

This is quite simple.

(4b-12) x (4b + 12) = 16b^2 - 144

because 4bx4b=16b^2, (4bx12)-(4bx12)=0, and 12x-12=-144.

This is called a difference of two squares, you just need to practice!

you think on reverse
(4b-12)(4b+12)=4b*4b+4b*12-12*4b-12*12
= 16b^2+48b-48b-144
= 16b^2-144
a^2-b^2=(a+b)(a-b)

Multiply out the brackets. use the 'crab's claw' method:-

Start with the left bracket, and multiply each term by the terms in the right bracket:-

(4b * 4b) + (4b * 12) + (-12 * 4b) + (-12 *12)

If you draw a curved line from 4b to 4b (4b*4b), and do that for each multiplication, you will get a 'crab's claw' - this sort of helps you remember the order of multiplication when you 'expand' two brackets like this.

Finishing off the sum above:-

16b² + 48b - 48b - 144

The 48b terms cancel each other out, giving:-

16b² - 144 as required.