Verify the factorization using the FOIL method. (x+3y)(x-7y)=x^{2}-7xy+3xy-21y^{2}=x^{2}-4xy-21y^{2}

Falak Kinney

Falak Kinney

Answered question

2021-05-30

Verify the factorization using the FOIL method.
(x+3y)(x7y)=x27xy+3xy21y2=x24xy21y2

Answer & Explanation

Margot Mill

Margot Mill

Skilled2021-05-31Added 106 answers

Step 1
The given expression is:
(x+3y)(x7y)=x27xy+3xy21y2=x24xy21y2
(x+3y)(x7y)=x24xy21y2...(1)
Thus, we have:
LHS=(x+3y)(x7y)
RHS=x24xy21y2
To verify the given expression i.e., equation (1).
Or,
To verify that LHS=RHS
Step 2
Using FOIL method to verify.
FOIL is First Outer Inner Last.
Thus, solving from LHS, we get:
((x)+(3y))((x)+(7y))
Here, we have:
First:(x)(x)
Outer: (x)(7y)
Inner: (3y)(x)
Last: (3y)(7y)
Thus, we have:
((x)+(3y))((x)+(7y))=(x)(x)+(x)(7y)+(3y)(x)+(3y)(7y)
Further simplifying, we have:
((x)+(3y))((x)+(7y))=x27xy+3xy21y2
(x+3y)(x7y)=x24xy21y2
LHS=x24xy21y2
Since, LHS=RHS
Hence the given factorization is verified.

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