Multiply (x + 3y + 5) by (2x\(^2\) + 5y + 2)
 

  • A 2x2 + 3yx2 + 10xy + 15y2 + 13y + 10x2 + 2x + 10
  • B 2x3 + 6yx2 + 5xy + 15y2 + 31y + 5x2 + 2x + 10
  • C 2x3 + 6xy2 + 5xy + 15y2 + 12y + 10x2 + 2x = 10
  • D 2x2 + 6xy2 + 5xy + 15y2 + 13y + 10x2 + 2x + 10
  • E 2x3 + 2yx2 + 10xy + 10y2 + 31y + 5x2 + 10
jamb 1978mathematics

The correct answer is B. 2x3 + 6yx2 + 5xy + 15y2 + 31y + 5x2 + 2x + 10

To multiply the expressions (x + 3y + 5) and (2x² + 5y + 2), we can use the distributive property of multiplication over addition, which states that for all real numbers a, b, and c, a*(b + c) = a*b + a*c.

Applying this property to each term in the first expression gives:

x * (2x² + 5y + 2) = 2x³ + 5xy + 2x
3y * (2x² + 5y + 2) = 6yx² + 15y² + 6y
5 * (2x² + 5y + 2) = 10x² + 25y + 10

Adding these results together gives:

2x³ + 6yx² + 10x² + 5xy + 15y² + 25y + 2x + 6y +10

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