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07/07/2021 11:14 am
Topic starter
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i) Volume : 3x2 – 12x
(ii) Volume : 12ky2 + 8ky – 20k
1 Answer
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07/07/2021 11:15 am
(i) Volume : 3x2–12x
3x2 – 12x can be written as 3x(x–4) by taking 3x out of both the terms.
Possible expression for length = 3
Possible expression for breadth = x
Possible expression for height = (x–4)
(ii) Volume: 12ky2 + 8ky – 20k
12ky2 + 8ky – 20k can be written as 4k(3y2+2y–5) by taking 4k out of both the terms.
12ky2 + 8ky – 20k = 4k(3y2+2y–5)
[Here, 3y2+2y–5 can be written as 3y2+5y–3y–5 using splitting the middle term method.]
= 4k(3y2+5y–3y–5)
= 4k[y(3y+5)–1(3y+5)]
= 4k(3y+5)(y–1)
Possible expression for length = 4k
Possible expression for breadth = (3y +5)
Possible expression for height = (y -1)