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Types of Expressions Based on the Number of Terms

Write ' T ' f...

Question

Write 'T' for true and 'F' for false
(i) In $- x$ , the constant term is $- 1$ .
(ii) The coefficient of $x$ in $x^{2} - 3 x + 5$ is $3$ .
(iii) $(5 x - 7) - (3 x - 5) = 2 x - 12$ .
(iv) $(3 x + 5 y) (3 x - 5 y) = (9 x^{2} - 25 y^{2})$ .
(v) If $a = 2$ and $b = 12$ , then the value of $a b (a^{2} + b^{2})$ is $414$ .

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Solution

(i)
Given polynomial function $- x = - x + 0$ .
So, the constant term is $0$ .
Thus, the constant term is $- 1$ is false.
Therefore, the given statement is false (F).
(ii)
Given polynomial $x^{2} - 3 x + 5$
The coefficient of $x$ is $- 3$ .
So, the coefficient of $x$ is $3$ is false.
Therefore, the given statement is false(F).
(iii)
Given equation $(5 x - 7) - (3 x - 5) = 2 x - 12$ .
LHS $= (5 x - 7) - (3 x - 5)$
$= 5 x (3 x - 5) + 7 (3 x - 5)$
$= 15 x^{2} - 25 x + 21 x - 35$
$= 15 x^{2} - 4 x - 35$
$\neq$ RHS
Therefore, the given statement is false(F).
(iv)
Given $(3 x + 5 y) (3 x - 5 y) = (9 x^{2} - 25 y^{2})$
LHS $= (3 x + 5 y) (3 x - 5 y)$
$= 3 x (3 x - 5 y) + 5 y (3 x - 5 y)$
$= 9 x^{2} - 15 x y + 15 x y - 25 y^{2}$
$= 9 x^{2} - 25 y^{2}$
$=$ RHS.
Therefore, the given statement is true(T).
(v)
If $a = 2$ and $b = 12$ , then the value of $a b (a^{2} + b^{2})$ is $414$ .
$a b (a^{2} + b^{2})$
$= 2 (12) (2^{2} + (12)^{2})$
$= 24 (4 + 144)$
$= 24 (148)$
$= 3552$
Therefore, the given statement is False (F).

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