Question

HELP PLEASE!
Factor Each Expression

54. -2h^2 + 4h + 70 =

68. w^2 + 24w + 144 =

70. 25x^2 - 36 =

Answer 1

@Michele_Laino

Answer 2

exercise #70
we have to apply this identity:
\[{a^2} - {b^2} = \left( {a - b} \right)\left( {a + b} \right)\]

Answer 3

where \(a^2=25, b^2=36\)

Answer 4

oops...\(a^2=25x^2\)

Answer 5

70. 25x^2 - 36 =

25x^2 - 36 right?

Answer 6

please, we have to express the left side as a product between two factors

Answer 7

Can you walk me threw it please? I don't understand what to do. You said a^2 - b^2 = (a - b) (a + b) So what do I do?

Answer 8

we have:
\[25{x^2} = {\left( {5x} \right)^2}\]
so if \(a^2=25x^2\) then \(a=5x\)

Answer 9

Okay, so

70. 25x^2 - 36 =

25x^2 = (5x)^2

Now what?

Answer 10

no, I'm sorry, we can write this:
\(36=6^2\)
so \(b^2=36\) then \(b=6\)

Answer 11

substituting into my formula above, i get:
\[25{x^2} - 36 = \left( {5x - 6} \right)\left( {5x + 6} \right)\]

Answer 12

70. 25x^2 - 36 =

25x^2 - 36 = (5x - 6) (5x + 6) Thats the answer?

Answer 13

yes!

Answer 14

Can you help me with the other two please

Answer 15

ok!

Answer 16

54. -2h^2 + 4h + 70 =

68. w^2 + 24w + 144 =

Answer 17

what is \((w+12)^2=...?\)

Answer 18

12w^2 ?

Answer 19

no, I'm sorry, it is a square of binomial, here is the rule:
the square of the first term--->\(w^2\)
the square of the second term--->\(12^2=144\)
the double product of the first term with the second term--->\(2\cdot w\cdot 12=24w\)
please add this three quantities, what do you get?

Answer 20

these*

Answer 21

68. w^2 + 24w + 144 =

24w, 144, w^2 ?

Answer 22

yes! you have to sum them each other, so you will get this:
\[{w^2} + 24w + 144 = {\left( {w + 12} \right)^2}\]

Answer 23

Thank you. So the answer is (w + 12)^2

Answer 24

correct!

Answer 25

exercise #54
we can rewrite your expression as below:
\[ - 2{h^2} + 4h + 70 = - 2\left( {{h^2} - 2h - 35} \right)\]

Answer 26

am I right?

Answer 27

How do you get -2h + 4h + 70 = -2 (h^2 - 2h - 35)

Answer 28

I divide each term by \(-2\)

Answer 29

divided*

Answer 30

and I factored out \(-2\)

Answer 31

Ok, so after you factored out -2, now what?

Answer 32

I got this:
\[ - 2{h^2} + 4h + 70 = - 2\left( {{h^2} - 2h - 35} \right)\]

Answer 33

And -2 (h^2 – 2h – 35) is the answer?

Answer 34

please, wait. Now, you have to try to search for two numbers, such that their sum is \(2\), and their product is \(-35\)

Answer 35

for example: \(-7\) and \(5\) can be the correct numbers?

Answer 36

they are not the correct numbers, right?

Answer 37

it should be 7 + -5

Answer 38

right! the correct numbers are \(7\) and \(-5\)

Answer 39

so, we can write this:

Answer 40

Okay what?

Answer 41

\[\begin{gathered}
- 2{h^2} + 4h + 70 = - 2\left( {{h^2} - 2h - 35} \right) = \hfill \\
\hfill \\
= - 2\left( {h - 7} \right)\left( {h - \left( { - 5} \right)} \right) = - 2\left( {h - 7} \right)\left( {h + 5} \right) \hfill \\
\end{gathered} \]

Answer 42

Okay, and -2 (h - 7) (h + 5) is the answer?

Answer 43

correct!

Answer 44

Thanks! Can you help me with a few more please?

Answer 45

ok!

Answer 46

please open a new question