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Maths-

General

Easy

Question

How can you use polynomial identities to multiply expressions ? 41 $cross times$ 39

hint Hint:

$left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis equals a squared minus b squared comma$ where a and b can be real number, variables or multiples of them.
We are asked to find on how you could use a polynomial identity to multiply the given expression.

The correct answer is: 1599

Step 1 of 2 :
The given expression is : 41 $cross times$ 39
It can be written as : (40 + 1)(40 - 1) which is same as the expression 41 $cross times$ 39.
Step 2 of 2 :
Now, apply the polynomial identity, $left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis equals a squared minus b squared text on end text left parenthesis 40 plus 1 right parenthesis left parenthesis 40 minus 1 right parenthesis$ to get the required answer:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell left parenthesis 40 plus 1 right parenthesis left parenthesis 40 minus 1 right parenthesis equals 40 squared minus 1 squared end cell row cell equals 1600 minus 1 end cell row cell equals 1599 end cell end table$

Polynomial identities are used to reduce the time and space while you solve higher degree polynomial expressions.

Related Questions to study

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

Any expression of the form $left parenthesis a plus b right parenthesis squared$ can be expanded using the identity $left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared$ rather than using the conventional and time taking method of multiplying them, $left parenthesis a plus b right parenthesis left parenthesis a plus b right parenthesis$ .

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

Any expression of the form $left parenthesis a plus b right parenthesis squared$ can be expanded using the identity $left parenthesis a plus b right parenthesis squared equals a squared plus a b plus b squared$ rather than using the conventional and time taking method of multiplying them, $left parenthesis a plus b right parenthesis left parenthesis a plus b right parenthesis$ .

Prove the difference of cubes identity : $a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.

Prove the difference of cubes identity : $a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.

Prove the sum of cubes identity : $a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.

Prove the sum of cubes identity : $a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

To prove an equation to be equal, we have to prove either the RHS is equal to the LHS or vice versa. The side should be selected based on the simplification process.

parallel

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

How can you use polynomial identities to multiply expressions ?
$open parentheses 2 x squared plus y cubed close parentheses squared$

Use polynomial identities to multiply the expressions ?
$left parenthesis x plus 6 right parenthesis squared$

Use polynomial identities to multiply the expressions ?
$left parenthesis x plus 6 right parenthesis squared$

Use polynomial identities to multiply the expressions ?
$left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis$

Use polynomial identities to multiply the expressions ?
$left parenthesis x minus 9 right parenthesis left parenthesis x minus 9 right parenthesis$

parallel

Prove the polynomial identity $x to the power of 4 minus y to the power of 4 equals left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis open parentheses x squared plus y squared close parentheses$

Prove the polynomial identity $x to the power of 4 minus y to the power of 4 equals left parenthesis x minus y right parenthesis left parenthesis x plus y right parenthesis open parentheses x squared plus y squared close parentheses$

Prove the difference of cubes identity :
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

Prove the difference of cubes identity :
$a cubed minus b cubed equals left parenthesis a minus b right parenthesis open parentheses a squared plus a b plus b squared close parentheses$

How could you use polynomial identities to factor the expression $x to the power of 6 minus y to the power of 6$ .

How could you use polynomial identities to factor the expression $x to the power of 6 minus y to the power of 6$ .

parallel

Prove the sum of cubes identity :
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

Prove the sum of cubes identity :
$a cubed plus b cubed equals left parenthesis a plus b right parenthesis open parentheses a squared minus a b plus b squared close parentheses$

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution.
b. After how many hours will the concentration of salt in the water be ?Round to the nearest hundredth.

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution.
b. After how many hours will the concentration of salt in the water be ?Round to the nearest hundredth.

Which function has a graph with a vertical asymptote at x = 3? Select all that apply .

Which function has a graph with a vertical asymptote at x = 3? Select all that apply .

parallel

Which function has a graph with a horizontal asymptote at y = -1.

Which function has a graph with a horizontal asymptote at y = -1.

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution .
a. What is the concentration of salt in the water after 4 hours?

After diluting salt water, the concentration of salt in the water is given by the function $f left parenthesis x right parenthesis equals fraction numerator 0.5 x over denominator x squared minus 1 end fraction$ , where x is the time in hours since the dilution .
a. What is the concentration of salt in the water after 4 hours?

A Software CD can be manufactured for $straight $ 0.10$ each. The development cost to produce the software is $straight $ 500 comma 000.$ . The first 200 CDs were used by testers to test the functionality of the software and were not sold.
a .Write a function f for the average cost , in dollars , of a sellable software CD , where x is the number of sellable software CDs
b. What are the vertical asymptotes of the graph ?
c. Graph the function

A Software CD can be manufactured for $straight $ 0.10$ each. The development cost to produce the software is $straight $ 500 comma 000.$ . The first 200 CDs were used by testers to test the functionality of the software and were not sold.
a .Write a function f for the average cost , in dollars , of a sellable software CD , where x is the number of sellable software CDs
b. What are the vertical asymptotes of the graph ?
c. Graph the function

parallel

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