Question

give me a please urget
${x}^{3} \times \frac{1}{2} ​ {x}^{2} \times −100x$
​

Answer 1

Step-by-step explanation:

x 3 - 2

1 3-2 2

1 - 3+2

=3-3

=u

Answer 2

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

(((x3) + (2•5x2)) - 100x) - 1000

STEP

2

:

Checking for a perfect cube

2.1 x3+10x2-100x-1000 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3+10x2-100x-1000

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: x3+10x2

Group 2: -100x-1000

Pull out from each group separately :

Group 1: (x+10) • (x2)

Group 2: (x+10) • (-100)

-------------------

Add up the two groups :

(x+10) • (x2-100)

Which is the desired factorization

Trying to factor as a Difference of Squares:

2.3 Factoring: x2-100

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 100 is the square of 10

Check : x2 is the square of x1

Factorization is : (x + 10) • (x - 10)

Multiplying Exponential Expressions:

2.4 Multiply (x + 10) by (x + 10)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (x+10) and the exponents are :

1 , as (x+10) is the same number as (x+10)1

and 1 , as (x+10) is the same number as (x+10)1

The product is therefore, (x+10)(1+1) = (x+10)2

Final result :

(x + 10)2 • (x - 10)

hope it helps

if not then sorry for this