math problems...?

Question

....and yes i am over 15...our neighbour has a math problem that we can't solve...pleeease help:

(3y+4)“ - 9(y+1)" = 79

" stays for 2....

pls help the old folks teaching the young!

kerrynell who do you get to the 24y and 18y ?

Answer 1

Ok, well first you want to expand each part.

(3y+4)^2 = (3y+4)(3y+4) = (9y^2 + 24y + 16) [Using FOIL -> multiply first, outer, inner then last)

9(y+1)^2 = 9(y+1)(y+1) = 9(y^2 + 2y +1) = 9y^2 + 18y + 9

Combine like terms...

9y^2 + 24y + 16 - 9y^2 - 18y - 9 = 6y + 7

Now solve for y...

6y + 7 = 79

6y = 72

y = 12


To double check...

(3(12) + 4)^2 - 9((12)+1)^2 = 79

(40)^2 - 9(13)^2 = 79

1600 - 1521 = 79

79 = 79

So y = 12.

Answer 2

(3y + 4)^2 - 9(y + 1)^2 = 79
Rewriting
(3y + 4)(3y + 4) -9(y+1)(y+1) = 79
Multiplying, or using the "Distributive Property" gives
3y(3y) + 3y(4) + 4(3y) + 4(4) -9(y^2 +y(1) + 1(y) + 1(1)) = 79
Multiplying and adding similar terms gives
9y^2 +12y + 12y + 16 - 9(y^2 +2y + 1) = 79
Multiplying, and adding similar terms gives
9y^2 + 24y + 16 -9y^2 -18y -9 = 79
Adding similar terms gives
6y + 7 = 79
Subtractinng 7 from both sides gives
6y = 72
Diving by 6 on both sides gives
Answer: y = 12

Answer 3

(3y + 4)^2 - 9(y + 1)^2 = 79
9y^2 + 24y + 16 - 9(y^2 + 2y + 1) = 79
9y^2 + 24y + 16 - 9y^2 - 18y - 9 = 79
24y + 16 - 18y - 9 = 79 [9y^2 gets cancelled]
6y + 7 = 79
6y = 79 - 7 = 72
y = 72/6 = 12

Formula: (a + b)^2 = a^2 + 2ab + b^2

Firstly, in (3y + 4)^2, a = 3y and b = 4.
So, (3y + 4)^2
= (3y)^2 + 2(3y)(4) + 4^2
= 9y^2 + 24y + 16

Next, a = y, b = 1.
So, (y + 1)^2 = y^2 + 2y + 1

Answer 4

(3y+4)(3y+4) - 9[(y+1)(y+1)] = 79
9y"+24y+16 - 9(y"+2y+1) = 79
9y"+24y+16 - 9y"-18y-9 = 79
6y+7 = 79
6y = 72
y = 12

Although the above answer of -12 was achieved incorrectly, it is also a possible answer. Because when you square y you will achieve a possitive number no matter what.

Answer 5

(3y+4)^2 - 9(y+1)^2 = 79
(3y+4)(3y+4) - 9(y+1)(y+1) = 79
9y^2 + 12y + 12y + 16 - 9(y^2 + y + y + 1) = 79
9y^2 + 24y + 16 - 9(y^2 + 2y + 1) = 79
9y^2 + 24y + 16 - 9y^2 + 18y + 9 = 79
9y^2 + 24y + 16 + -9y^2 + 18y + 9 = 79
9y^2 + -9y^2 + 24y + 18y + 16 + 9 = 79
24y + 18y + 16 + 9 = 79
42y + 16 + 9 = 79
42y + 25 = 79
42y = 54
y = 54/42

Answer 6

(9y^2 + 24y + 16) - 9(y^2 + 2y + 1) = 79
9y^2 + 24y + 16 - 9y^2 - 18y - 9) = 79
6y + 7 = 79
6y = 72
y = 12

Answer 7

multiply it out:

9y'' + 24y + 16 - 9y'' - 18y - 9 = 79
6y + 7 = 79
6y = 72
y = 72/6 = 36/3 = 12