Question

$\huge{\mathfrak{\pink{☆Question ☆}}}$

Choose the correct algebraic expression from the following option for the factor given in the box.

${\underline{\underline{\boxed{\sf{\red{(3x-y)(x+y)² }}}}}}$

✦✧ Option✧✦
A) 3x³- 5x² y- 2xy² +y³
B) 3x³- 7x² y- xy² +3y³
C) 3x³- 7x² y- 5xy² +y³
D) 3x³- 5x² y- xy² +y³​

Answer 1

Given :-

• ( 3x - y)(x + y )²

To Find :-

• Expand it to match from the given options

Solution :-

$\sf \leadsto (3x-y)(x+y)^{2}$

$\sf \leadsto (3x-y)(x^{2} + 2xy +y^{2} )$

$\sf \leadsto 3x^{3} + 6x^{2}y + 3xy^{2} -yx^{2} - 2xy^{2} - y^{3}$

$\sf \leadsto 3x^{2} + 6x^{2}y + 3xy^{2} -x^{2}y - 2xy^{2} - y^{3}$

$\sf \leadsto 3x^{3} + 6x^{2}y - x^{2}y + 3xy^{2} - 2xy^{2} - y^{3}$

$\sf \leadsto 3x^{3} + 5x^{2}y + xy^{2} - y^{3}$

Answer 2

$\huge{\mathfrak{\pink{Correct\:Question♡ }}}$

Simplify-:

• ${\underline{\underline{\boxed{\sf{\red{(3x-y)(x+y)² }}}}}}$

$\huge{\mathfrak{\blue{AnswEr ♡}}}$

• ${\underline{\underline{\boxed{\sf{\red{(3x-y)(x+y)²=3x³+5x²y+xy²-y³ }}}}}}$

Explanation-:

• ${\underline{\underline{\boxed{\sf{\red{(3x-y)(x+y)² }}}}}}$

Now-:

• $\sf{\implies {\large{ (3x-y)(x+y)² }}}$

• $\sf{\implies {\large{ (3x-y)(x²+2xy+y²) \:\:\:\:}}} \\\\ \sf{\large{Applying \:= (a+b)² = a² + 2ab + b²}}$

• $\sf{\implies {\large{ 3x(x²+2xy+y²)-y(x²+2xy+y²) \:\:\:\:}}}$

• $\sf{\implies {\large{ 3x³+6x²y+3xy²-x²y-2xy²-y³) \:\:\:\:}}}$

• $\sf{\implies {\large{ 3x³+6x²y-x²y+3xy²-2xy²-y³) \:\:\:\:}}}$

• $\sf{\implies {\large{ 3x³+5x²y+xy²-y³) \:\:\:\:}}}$

Hence ,

• ${\underline{\underline{\boxed{\sf{\red{(3x-y)(x+y)²=3x³+5x²y+xy²-y³ }}}}}}$

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