Question

simplify the following expressions (xy+yz)²-(xy-yz)²​

Answer 1

Answer:

(xy+yz)²-(xy-yz)²

= x²y²+y²z² -x²y²-y²z²

= 0

hope this helps you !!!

Answer 2

Given :

• (xy + yz)² - (xy - yz)²

Solution :

• Method : 1

Apply identity

• a² - b² = (a + b)(a - b)

• (xy + yz) = a
• (xy - yz) = b

→ (xy + yz)² - (xy - yz)²

→ (xy + yz + xy - yz)[(xy + yz) - ( xy - yz)]

→ (xy + yz + xy - yz)(xy + yz - xy + yz)

→ (xy + xy + yz - yz)(xy - xy + yz + yz)

→ 2xy × 2yz

→ 4xy²z

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• Method : 2

Apply identity

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab

→ (xy+yz)²- (xy-yz)²

→ (xy)² + (yz)² + 2*xy*yz - [(xy)² + (yz)² - 2*xy*yz]

→ x²y² + y²z² + 2xy²z - x²y² - y²z² + 2xy²z

→ x²y² - x²y² + y²z² - y²z² + 2xy²z + 2xy²z

→ 4xy²z

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