###### Advertisements

###### Advertisements

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

Volume : 3x^{2} – 12x |

###### Advertisements

#### Solution

Volume of cuboid = Length × Breadth × Height

The expression given for the volume of the cuboid has to be factorised. One of its factors will be its length, one will be its breadth, and one will be its height.

3x^{2} – 12x = 3x(x - 4)

Possible expression for length* = 3*

Possible expression for breadth *= x*

Possible expression for height* = (x – 4)*

#### APPEARS IN

#### RELATED QUESTIONS

Evaluate the following using suitable identities:- (998)^{3}

Factorise :- 8a^{3} – b^{3} – 12a^{2}b + 6ab^{2}

If x + y + z = 0, show that x^{3} + y^{3} + z^{3} = 3xyz.

Without actually calculating the cubes, find the value of the following:- (28)^{3} + (–15)^{3} + (–13)^{3}

Simplify the following products:

`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`

Write in the expanded form: `(x + 2y + 4z)^2`

If 3x − 2y = 11 and xy = 12, find the value of 27x^{3} − 8y^{3}

Evaluate of the following:

93^{3} − 107^{3}

Find the following product:

(7p^{4} + q) (49p^{8} − 7p^{4}q + q^{2})

Find the following product:

\[\left( \frac{3}{x} - \frac{5}{y} \right) \left( \frac{9}{x^2} + \frac{25}{y^2} + \frac{15}{xy} \right)\]

If a + b + c = 9 and ab +bc + ca = 26, find the value of a^{3} + b^{3}+ c^{3} − 3abc

If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]

If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]

If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =

If \[\frac{a}{b} + \frac{b}{a} = 1\] then a^{3} + b^{3} =

If a - b = 4 and a + b = 6; find

(i) a^{2} + b^{2}(ii) ab

If a^{2} - 5a - 1 = 0 and a ≠ 0 ; find :

(i) `a - 1/a`

(ii) `a + 1/a`

(iii) `a^2 - 1/a^2`

**Use direct method to evaluate the following products :**

(x + 8)(x + 3)

**Use the direct method to evaluate the following products :**

(y + 5)(y – 3)

**Use the direct method to evaluate the following products :**

(b – 3) (b – 5)

**Use the direct method to evaluate the following products :**

(5a + 16) (3a – 7)

**Use the direct method to evaluate :**

(4+5x) (4−5x)

**Evaluate: **(2a + 0.5) (7a − 0.3)

**Evaluate: **`(2"x"-3/5)(2"x"+3/5)`

**Evaluate: **`(4/7"a"+3/4"b")(4/7"a"-3/4"b")`

**Evaluate: **(6 − 5xy) (6 + 5xy)

**Evaluate: **203 × 197

Evaluate the following without multiplying:

(95)^{2}

Evaluate, using (a + b)(a - b)= a^{2} - b^{2}.

4.9 x 5.1

If p + q = 8 and p - q = 4, find:

pq

If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :

`"a" + (1)/"a"`

If a^{2} - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`

If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`

If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.

Simplify:

(x + y - z)^{2} + (x - y + z)^{2}

If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x^{3} – y^{3} is ______.

Factorise the following:

16x^{2} + 4y^{2} + 9z^{2} – 16xy – 12yz + 24xz

If a + b + c = 9 and ab + bc + ca = 26, find a^{2} + b^{2} + c^{2}.

Multiply x^{2} + 4y^{2} + z^{2} + 2xy + xz – 2yz by (– z + x – 2y).