factorise 36x^2+84x+49
Answers
Answer:
see the attached image
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Step-by-step explanation:
To factor this expression, first notice that the first and last coefficients (the numbers multiplying the variable; for example the coefficient of 64x is simply 64) are perfect squares. 36 is 6 squared and 49 is 7 squared. Although there could be other combinations, this is the most likely one because it is neat and simple. So the factored form now looks like this: (6x ? 7)(6x ? 7) where the question mark represents a plus or minus sign. Since the middle term determines whether the sign is positive or negative, look at it. -84x indicates the signs should be both negative because that is the only way to get a middle negative term and a positive last term. So that yields (6x-7)(6x-7) or simplified:
(
6
x
−
7
)
2
Check FOIL
(6x-7)(6x-7)
(6x)(6x) + (6x)(-7) + (6x)(-7) + (-7)(-7)
36
x
2
- 42x - 42x + 49
36
x
2
-84 x + 49