
How do you factor the expression ?
Answer
463.8k+ views
Hint: The given equation is a quadratic equation. To factorize a quadratic equation we have to write bx as mx + nx such that product of m and n is equal to product of ac. In the equation we have to write 60b = mb + nb such that mn is equal to – 1600. We can evaluate m is 80 and n is – 20.
Complete step by step solution:
The given equation is
If we compare it with we get a = 16, b = 60 and c = - 100
The value of ac is equal to – 1600
So, we have to find 2 numbers such that their sum is 60 and product is – 1600. The numbers are 80 and – 20
So, we can write
We can take 16b common from first 2 terms and – 20 common from last 2 terms
Now we can take b + 5 common from the whole equation
Now we can take 4 common from 16b – 20
is the factored form of the equation .
Note: The graph of all quadratic equations is a parabola whose axis is always parallel to y axis. In quadratic equation , if a is greater than 0 then it will be upward parabola and if a is less than 0 then graph will be downward parabola. If the discriminant ( ) is less than 0 then the parabola will never touch the x axis.
Complete step by step solution:
The given equation is
If we compare it with
The value of ac is equal to – 1600
So, we have to find 2 numbers such that their sum is 60 and product is – 1600. The numbers are 80 and – 20
So, we can write
We can take 16b common from first 2 terms and – 20 common from last 2 terms
Now we can take b + 5 common from the whole equation
Now we can take 4 common from 16b – 20
Note: The graph of all quadratic equations is a parabola whose axis is always parallel to y axis. In quadratic equation
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