factorise the following
Answers
Answer:
e. (a+b)⁴-(a-b)⁴.
(a+b)⁴=a⁴+4a³b+6a²b²+4ab³+b⁴.
(a-b)⁴=a⁴-4a³b+6a²b²-4ab³+b⁴.
(a+b)⁴-(a-b)⁴=(a⁴+4a³b+6a²b²+4ab³+b⁴)-(a⁴-4a³b+6a²b²-4ab³+b⁴).
(a+b)⁴-(a-b)⁴=a⁴+4a³b+6a²b²+4ab³+b⁴-a⁴+4a³b-6a²b²+4ab³-b⁴.
(a+b)⁴-(a-b)⁴=4a³b+4ab³+4a³b+4ab³.
(a+b)⁴-(a-b)⁴=8a³b+8ab³.
f. 16x^5-81x.
x(16x⁴-81).
x(((4x)²)²-(9)²).
x((4x²+9)(4x²-9)).
x((2x)²-(3)²).
x((2x+3)(2x-3)).
x(2x+3)(2x-3).
g. x²+11x+24=0.
x²+8x+3x+24=0.
x(x+8)+3(x+8)=0.
(x+3)(x+8)=0.
x+3=0. & x+8=0.
x=-3. & x=-8.
h. x²+15x+54=0.
x²+9x+6x+54=0.
x(x+9)+6(x+9)=0.
(x+6)(x+9)=0.
x+6=0. & x+9=0.
x=-6. & x=-9.
i. x²+20x+84=0.
x²+14x+6x+84=0.
x(x+14)+6(x+14)=0.
(x+6)(x+14)=0.
x+6=0. & x+14=0.
x=-6. & x=-14.
j. x²-17x+72.
x²-9x-8x+72=0.
x(x-9)-8(x-9)=0.
(x-8)(x-9)=0.
x-8=0. & x-9=0.
x=8. & x=9.
I think this is your answer.
ANSWER e):
We can write it as,
We know that,
⇒ x² - y² = (x - y)(x + y)
So,
Similarly,
We know that,
⇒ (x ± y)² = x² + y² ± 2xy
So,
Now,
On simplifying,
Taking 2 common,
OR
ANSWER f):
Taking x common,
We can write it as,
So,
Also,
Hence,
Therefore,
ANSWER g):
On splitting the middle term,
Taking common,
Taking (x + 8) common,
ANSWER h):
On splitting the middle term,
Taking common,
Taking (x + 6) common,
ANSWER i):
On splitting the middle term,
Taking common,
Taking (x + 14) common,
ANSWER j):
On splitting the middle term,
Taking common,
Taking (x - 8) common,