What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)

1 answer:

8 0

Use distributie property which is
a(b+c)=ab+ac
therefor
6x(x-4)=6x^2-24x

distribute the negative 1 infroont of the (9x-1)
-1(9x-1)=-9x+1
now we have

6x^2-24x-16x^2-9x+1
gropu like terms
6x^2-16x^2-24x-9x+1
add like terms
-10x^2-33x+1 is simplest form

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The sum of a 3 digit number and a 1 digit number is 217. The product of the numbers is 642. If one number is between 200 and 225

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Let, the numbers be "x" and "y". Consider "x" as the triple digit number.
Now, according to the question,
x + y = 217..........................equation (1)

x * y = 642............................equation (2)

Now,
Taking equation (2),
x * y = 642
y = 642 / x..................................equation (3)

Now, Taking equation (1),
$x+y=217$

Substituting the value of y from equation (3), we get,

$x+ \frac{642}{x} =217$

$\frac{x *x+642}{x} =217$

$x^{2} +642 =217*x$

$x^{2} +642 =217x$

$x^{2} +642-217x =0$

$x^{2} -217x+642 =0$

$x^{2} -3x-214x+642 =0$

$x(x-3)-214(x-3)=0$

$(x-3)(x-214)=0$

Using zero product property,
EITHER,
x - 3 = 0
x = 3
OR,
x - 214 = 0
x = 214
Since, "x" is the triple digit number, x = 214.
Now,
Taking equation (2),
x * y = 642
Substituting the value of "x" in the equation, we get,
(214) * y = 642
y = 642 / 214
y = 3

So, the numbers are 214 and 3.

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