Question

M veyy upset...not getting any satisfaction frm d answers..
Let's see whether I satisfy frm ur answer or not.
y² - b²- 8b - 16
Factorise it completely....​

Answer 1

Question :-- Factorise y² - b² - 8b - 16 .

Concept used :--

Splitting the middle term method :--- In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term.

1) Find the product of 1st and last term( a x c). two new factors, including the proper signs. terms and the last two terms.

→ Algebra Formula :- (a² - b²) = (a+b)(a-b)

→ Taking Negative common Outside bracket will change all sign ..

→ If we want to Factorise , take it first Equal to zero .

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Solution :---

→ y² - b² - 8b - 16 = 0

→ y² - 1[ b² + 8b + 16 ] = 0 ( taking -1 common )

Now, Splitting the middle term , from b² + 8b + 16 .

Here , we have,

a = 1 , b = 8 , c = 16 ,

→ sum of roots = b

→ Product of roots = a*c = 1*16 = 16 ,

So, we have to Think of Two numbers whose multiple is 16 and when we add both we get 8 .

→ 4 and 4 are such numbers..

So,

→ y² - 1[ b² + 8b + 16 ] = 0

→ y² - (b² + 4b + 4b + 16) = 0

→ y² - [b(b+4) + 4(b+4)] = 0 (Taking common)

→ y² - [(b+4)(b+4)] = 0 (Taking (b+4) common)

→ y² - [(b+4)²] = 0

or,

→ y² - (b+4)² = 0

Now, using (a² - b²) = (a+b)(a-b) we get,

→ (y+b+4)(y-b-4) = 0

Hence, Simplest Factorize Form of given Equation is (y+b+4)(y-b-4) ...

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If we want to Find value of y , put both Equal to zero now , and we can find both ,

if y+b+4 = 0

→ y = -b - 4 = -(b+4)

and , if y - b -4 = 0

→ y = (b + 4)

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Answer 2

Answer:

Factorize Form of Equation = ( y - b - 4 )( y + b + 4 )

Step-by-step explanation:

We Have :-

y² - b² - 8b - 16

To Do :-

Factorise it

Formula / Method Used :-

( a + b )² = a² + b² + 2ab

a² - b² = ( a + b )( a - b )

Solution :-

$y^{2}-( b^{2} +8b + 16 )\\\\y^{2} -(b^{2} +8b +4^{2} )\\\\y^{2}-[(b+4)^{2} ]\\\\(y-b-4)(y+b+4)$

Factorize Form of Equation = ( y - b - 4 )( y + b + 4 )