Question

Using factorisation find weather (A square + 2AB + B square) — (a Square +2 AC + C Square) is divisible by 2A + B + C. Also find the quotient.

Answer 1

Step-by-step explanation:

$\scriptsize(A² + 2AB + B² ) – (A² + 2AC + C²) ÷ 2A + B + C$

$\frac{(A² + 2AB + B² ) – (A² + 2AC + C²) }{2A + B + C}$

$\frac{A² + 2AB + B² – A² - 2AC - C²}{2A + B + C}$

$\frac{ B²- C² + 2AB - 2AC }{2A + B + C}$

$\frac{ (B + C)(B - C) + 2A(B - C) }{2A + B + C}$

$\frac{ [(B + C) + 2A][B - C] }{2A + B + C}$

Answer 2

Answer:

Applying the identities: a

2

−b

2

=(a+b)(a−b) and (a+b)

2

=a

2

+b

2

+2ab

Using the above identities, the equation a

2

+2ab+b

2

−9c

2

can be factorised as follows:

a

2

+2ab+b

2

−9c

2

=(a+b)

2

−9c

2

=(a+b)

2

−(3c)

2

=(a+b+3c)(a+b−3c)

Hence, a

2

+2ab+b

2

−9c

2

=(a+b+3c)(a+b−3c)