Simplyfying $(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$ algebraic experssion Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Problems and Resources to self-study medium level mathHow to simplify an equation of the $(x^2 + y^2)^1/2$ For example:Ascertaining a from logarithmic equationsCubic polynomial missing the linear termCoverting denary numbers into octal, binary and hexadecimal formStumped by a pretty basic fraction divisionHow do we get from $ln A=ln P+rn$ to $A=Pe^rn$ and similar logarithmic equations?How do I get from log F = log G + log m - log(1/M) - 2 log r to a solution withoug logs?Dividing higher-order algebraic expressionsSimplifying a polynomial
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Simplyfying $(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$ algebraic experssion
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Problems and Resources to self-study medium level mathHow to simplify an equation of the $(x^2 + y^2)^1/2$ For example:Ascertaining a from logarithmic equationsCubic polynomial missing the linear termCoverting denary numbers into octal, binary and hexadecimal formStumped by a pretty basic fraction divisionHow do we get from $ln A=ln P+rn$ to $A=Pe^rn$ and similar logarithmic equations?How do I get from log F = log G + log m - log(1/M) - 2 log r to a solution withoug logs?Dividing higher-order algebraic expressionsSimplifying a polynomial
$begingroup$
I've been self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am on the (precalculus) Algebra section. (And I've been asking lots of questions here as well!) I'm trying to simplify an algebraic expression, and I've tried it 101 ways, but I just can't seem to get a reasonable result. The polynomial is:
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
Can anyone help me out? These are really making me feel dumb.
algebra-precalculus self-learning
asked Mar 26 at 16:29
neuronneuron
22917
$endgroup$
add a comment |
$begingroup$
I've been self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am on the (precalculus) Algebra section. (And I've been asking lots of questions here as well!) I'm trying to simplify an algebraic expression, and I've tried it 101 ways, but I just can't seem to get a reasonable result. The polynomial is:
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
Can anyone help me out? These are really making me feel dumb.
algebra-precalculus self-learning
asked Mar 26 at 16:29
neuronneuron
22917
$endgroup$
$begingroup$
Hint: $(x^2-y^2)=(x-y)cdot (x+y)$ I think you can finish.
$endgroup$
– callculus
Mar 26 at 16:31
add a comment |
$begingroup$
I've been self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am on the (precalculus) Algebra section. (And I've been asking lots of questions here as well!) I'm trying to simplify an algebraic expression, and I've tried it 101 ways, but I just can't seem to get a reasonable result. The polynomial is:
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
Can anyone help me out? These are really making me feel dumb.
algebra-precalculus self-learning
asked Mar 26 at 16:29
neuronneuron
22917
$endgroup$
I've been self-studying from Stroud & Booth's amazing "Engineering Mathematics", and am on the (precalculus) Algebra section. (And I've been asking lots of questions here as well!) I'm trying to simplify an algebraic expression, and I've tried it 101 ways, but I just can't seem to get a reasonable result. The polynomial is:
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
Can anyone help me out? These are really making me feel dumb.
algebra-precalculus self-learning
algebra-precalculus self-learning
asked Mar 26 at 16:29
neuronneuron
22917
asked Mar 26 at 16:29
neuronneuron
22917
asked Mar 26 at 16:29
neuronneuron
22917
asked Mar 26 at 16:29
neuronneuron
22917
asked Mar 26 at 16:29
neuronneuron
22917
22917
$begingroup$
Hint: $(x^2-y^2)=(x-y)cdot (x+y)$ I think you can finish.
$endgroup$
– callculus
Mar 26 at 16:31
add a comment |
$begingroup$
Hint: $(x^2-y^2)=(x-y)cdot (x+y)$ I think you can finish.
$endgroup$
– callculus
Mar 26 at 16:31
$begingroup$
Hint: $(x^2-y^2)=(x-y)cdot (x+y)$ I think you can finish.
$endgroup$
– callculus
Mar 26 at 16:31
$begingroup$
Hint: $(x^2-y^2)=(x-y)cdot (x+y)$ I think you can finish.
$endgroup$
– callculus
Mar 26 at 16:31
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12times(x+y)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12+frac32$$
$$=(x-y)^2.$$
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
$endgroup$
add a comment |
$begingroup$
Since $x^2-y^2=(x+y)(x-y)$, $(x^2-y^2)^frac12=(x+y)^frac12(x-y)^frac12$. Therefore, your expression is equal to$$(x-y)^frac12+frac32=(x-y)^2.$$
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
$endgroup$
add a comment |
$begingroup$
Write your term in the form
$$fracsqrt(x-y)(x+y)sqrt(x-y)^3 sqrtx+y$$
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12times(x+y)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12+frac32$$
$$=(x-y)^2.$$
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
$endgroup$
add a comment |
$begingroup$
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12times(x+y)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12+frac32$$
$$=(x-y)^2.$$
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
$endgroup$
add a comment |
$begingroup$
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12times(x+y)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12+frac32$$
$$=(x-y)^2.$$
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
$endgroup$
$$(x^2-y^2)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12times(x+y)^frac12times(x-y)^frac32times(x+y)^frac-12$$
$$=(x-y)^frac12+frac32$$
$$=(x-y)^2.$$
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
answered Mar 26 at 16:48
saket kumarsaket kumar
167113
167113
add a comment |
add a comment |
$begingroup$
Since $x^2-y^2=(x+y)(x-y)$, $(x^2-y^2)^frac12=(x+y)^frac12(x-y)^frac12$. Therefore, your expression is equal to$$(x-y)^frac12+frac32=(x-y)^2.$$
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
$endgroup$
add a comment |
$begingroup$
Since $x^2-y^2=(x+y)(x-y)$, $(x^2-y^2)^frac12=(x+y)^frac12(x-y)^frac12$. Therefore, your expression is equal to$$(x-y)^frac12+frac32=(x-y)^2.$$
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
$endgroup$
add a comment |
$begingroup$
Since $x^2-y^2=(x+y)(x-y)$, $(x^2-y^2)^frac12=(x+y)^frac12(x-y)^frac12$. Therefore, your expression is equal to$$(x-y)^frac12+frac32=(x-y)^2.$$
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
$endgroup$
Since $x^2-y^2=(x+y)(x-y)$, $(x^2-y^2)^frac12=(x+y)^frac12(x-y)^frac12$. Therefore, your expression is equal to$$(x-y)^frac12+frac32=(x-y)^2.$$
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
answered Mar 26 at 16:31
José Carlos SantosJosé Carlos Santos
175k24134243
175k24134243
add a comment |
add a comment |
$begingroup$
Write your term in the form
$$fracsqrt(x-y)(x+y)sqrt(x-y)^3 sqrtx+y$$
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
$endgroup$
add a comment |
$begingroup$
Write your term in the form
$$fracsqrt(x-y)(x+y)sqrt(x-y)^3 sqrtx+y$$
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
$endgroup$
add a comment |
$begingroup$
Write your term in the form
$$fracsqrt(x-y)(x+y)sqrt(x-y)^3 sqrtx+y$$
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
$endgroup$
Write your term in the form
$$fracsqrt(x-y)(x+y)sqrt(x-y)^3 sqrtx+y$$
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
answered Mar 26 at 16:34
Dr. Sonnhard GraubnerDr. Sonnhard Graubner
79.1k42867
79.1k42867
add a comment |
add a comment |
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Hint: $(x^2-y^2)=(x-y)cdot (x+y)$ I think you can finish.
$endgroup$
– callculus
Mar 26 at 16:31