Question

8k^4 -3k^2 multiplied by 5k^2

Answer 1

Answer: 40k⁶-15k⁴

Step-by-step explanation:

$(8k^4-3k^2)(5k^2)=\\\\8k^4(5k^2)-3k^2(5k^2)=\\\\8(5)(k^{4+2})-3(5)(k^{2+2})=\\\\40k^6-15k^4$

Answer 2

Result of $8k^{4} -3k^{2}$ multiplied by $5k^{2}$ is $40k^{6}-15 k^{4}$

Algebra and Exponent

To answer this question you need to know about algebra and exponent rule.

$8k^{4} -3k^{2}$ multiplied by $5k^{2}$

It means the operation will become:

$5k^{2} (8k^{4} -3k^{2} )=$

• First, $8k^{4} -3k^{2}$ can't be calculate because of different variable. Even though they both use the letters '$k$', $k^{4}$ dan $k^{2}$ cannot be added because they have different powers. In algebraic addition, addition can only be done on the same variables and which have the same power.

• Because $8k^{4} -3k^{2}$ can not be calculated, then we directly calculate the multiplication $5k^{2} (8k^{4} -3k^{2} )$

The way to calculate algebraic multiplication with 2 or more variables is the way I call 'rainbow'.

$5k^{2} (8k^{4} -3k^{2} )=$

$5k^{2}$ multiplied by $8k^{4}$,  $5k^{2}$ multiplied by $-3k^{2}$ first, then the two are added.

• Let's multiply one by one first

$(5k^{2}) (8k^{4} )=$

The way to multiply this is by: numbers multiplied by numbers and letters multiplied by letters

$=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )$

Then how to multiply the letters, this uses the rule of exponents. If there are 2 same variables are multiplied, then the result is a variable with the power of the sum of the two powers.

$a^{m} a^{n} =a^{m+n}$

Which means,

$k^{2}k^{4} =k^{6}$

Then,

$=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )\\=40k^{6}$

Also same with above,

$=(5k^{2} )(-3k^{2} )\\=((5)(-3))((k^{2} )(k^{2} )\\=-15k^{4}$

• Add the result of two operation above

$=5k^{2} (8k^{4} -3k^{2} )\\=((5k^{2})(8k^{4})+((5k^{2})(-3k^{2})\\=(40k^{6})+(-15k^{4} )\\=40k^{6}-15k^{4}$

Learn more about algebra multiplication here: https://brainly.ph/question/72890

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