Find the product:(2x2 – 5y2) (x2 + 3y2)

1.	Find the product:(2x2 – 5y2) (x2 + 3y2)
Answer» (2x² – 5y²) (x² + 3y²) Suppose (a – b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below. (a – b) × (c + d) = a × (c + d) – b × (c + d) = (a × c + a × d) – (b × c + b × d) = ac + ad – bc – bd Let, a= 2x², b= 5y², c= x², d= 3y² Now, = 2x² × (x² + 3y²) – 5y² × (x² + 3y²) = [(2x² × x²) + (2x² × 3y²)] – [(5y² × x²) + (5y² × 3y²)] = [2x⁴ + 6x²y² – 5y²x² – 15y⁴] = [2x⁴ + x²y² – 15y⁴]

Answer»

(2x² – 5y²) (x² + 3y²)

Suppose (a – b) and (c + d) are two binomials. By using the distributive law of multiplication over addition twice, we may find their product as given below.

(a – b) × (c + d) = a × (c + d) – b × (c + d) = (a × c + a × d) – (b × c + b × d)

= ac + ad – bc – bd

Let,

a= 2x², b= 5y², c= x², d= 3y²

Now,

= 2x² × (x² + 3y²) – 5y² × (x² + 3y²)

= [(2x² × x²) + (2x² × 3y²)] – [(5y² × x²) + (5y² × 3y²)]

= [2x⁴ + 6x²y² – 5y²x² – 15y⁴]

= [2x⁴ + x²y² – 15y⁴]

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Find the product:(2x2 – 5y2) (x2 + 3y2)

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