A couple more:
If two adjacent sides of a rectangle are (5x2 + 25xy + 4y2) and (2x2 – 2xy + 3y2), find its area
Area of a rectangle is just the product of its adjacent sides:
Area = (5x2 + 25xy + 4y2)(2x2 - 2xy + 3y2)
= 5x2 *(2x2 - 2xy + 3y2) + 25xy*(2x2 - 2xy + 3y2) + 4y2*(2x2 - 2xy + 3y2)
= 10x4 - 10x3y +15x2y2 + 50x3y -50 x2y2 +75xy3 + 8x2y2 - 8 xy3 + 12y4
I'll leave you to simplify this by collecting like terms together.
A two digit number is three times the sum of its digits. If 45 is added to the number; its digits are reversed. Find the number
A two digit number can be represented as 10a + b where a and b are single digits (a>0).
So: 10a + b = 3(a + b) ...(1)
10a + b + 45 = 10b + a ...(2)
From (1): 10a + b = 3a + 3b or 7a - 2b = 0 ...(3)
From (2): 9a - 9b = -45 or a - b = -5 ...(4)
From (4) we have a = b - 5 ...(5)
Use (5) in (3): 7(b-5) - 2b = 0 or 7b - 35 - 2b = 0 or 5b = 35 so b = 7.
Put this back into (5): a = 7 - 5 or a = 2.
So the original 2-digit number was 27
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