please answer this please
Answers
Answer:
1. (2x+9) x (x+3)
2. (x-2) (x+2) (x^2 + 4)
3. -90
Step-by-step explanation:
1. Factorise: 2x^2 + 15x + 27
--> Since, we know that for this question we need to find the two numbers whose sum is 15 and product is 54 (2x27 = 54)
Therefore, we can chose 9 and 6 as our numbers
Therefore, by splitting the middle term method, (ax^2 + bx + c)
We get, --> 2x^2 + 9x + 6x + 27
On further simplifying it, --> x(2x + 9) + 3(2x + 9)
--> (2x+9) x (x+3)
So, 2x^2 + 15x + 27 = (2x+9) x (x+3)
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2. Factorise x^4 - 16
--> [Theorum used over here:- x^2 + y^2 = (x+y) (x-y) ]
x^4 -16 = (x^2 - 4) (x^2 + 4)
= (x-2) (x+2) (x^2 + 4)
(Note:- (x^2 + 4) can be further factorised but even if you kept the answer till this portion also, it will be correct.)
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3. Evaluate 10^3 - 15^3 + 5^3
--> = 5 (2^3 - 3^3 + 1^3) (Taking 5 as common)
= 5 (8 - 27 + 1)
= 5 x (-18)
= -90
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