# NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.4

These NCERT Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.4 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 14 Factorization Exercise 14.4

Question 1.
Find and correct the errors in the following mathematical statements.
(1) 4(x – 5) = 4x – 5
The given statement is incorrect.
The correct statement is
4(x – 5) = 4x – 20

(2) x (3x + 2) = 3x2 + 2
The given statement is incorrect.
The correct statement is x (3x + 2) = 3x2 + 2x

(3) 2x + 3y = 5xy
This is an incorrect statement.
The correct statement is 2x + 3y = 2x + 3y

(4) x + 2x + 3x = 5x
This is an incorrect statement.
The correct statement is x + 2x + 3x = 6x

(5) 5y + 2y + y – 7y = 0
This is an incorrect statement.
The correct statement is
5y + 2y + y – 7y = y

(6) 3x + 2x = 5x2
This is an incorrect statement.
The correct statement is 3x + 2x = 5x

(7) (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7
This given statement is incorrect.
The correct statement is
(2x)2 + 4 (2x) + 7 = 4x2 + 8x + 7

(8) (2x)2 + 5x = 4x + 5x = 9x2
The given statement is incorrect.
The correct statement is (2x)2 + 5x = 4x2 + 5x

(9) (3x + 2)2 = 3x2 + 6x + 4
The given statement is incorrect.
The correct statement is
(3x + 2)2 = (3x)2 + 2 × 3x × 2 + (2)2
(3x + 2)2 = 9x2 + 12x + 4

(10) Substituting x = – 3 in
(a) x2 + 5x + 4
= (- 3)2 + 5 (-3) + 4
= 9 + 2 + 4
= 15
The given statement is incorrect.
The correct statement is x2 + 5x + 4
= (-3)2 + 5 (- 3) + 4
= 9 – 15 + 4
= 13 – 15 = – 2
∴ x2 + 5x + 4 = -2 at x = – 3

(b) x2 – 5x + 4
= (-3)2 – 5 (-3) + 4
= 9 – 15 + 4 = -2
The given statement is incorrect.
The correct statement is
x2 – 5x + 4
= (-3)2 – 5 (-3) + 4
= 9 + 15 +4 = 28

(c) x2 + 5x = (-3)2 + 5 (-3)
= – 9 – 15 = – 24
The given statement is incorrect.
The correct statement is
x2 + 5x
= (-3)2 + 5(—3)
= 9 – 15 = -6

(11) (y – 3)2 = y2 – 9
The given statement is incorrect. (y-3)2
= y2 – 2 (y) (3) + 32
= y2 – 6y + 9
The correct statement is (y – 3)2 = y2 – 6y + 9

(12) (z + 5)2 = z2 + 25
The given statement is incorrect.
(z + 5)2 = z2 + 2 × z × 5 + 52
= z2 + 10z + 25
The correct statement is (z + 5)2 = z2 + 10z + 25

(13) (2a + 3b) (a – b) = 2a2 – 3b2
The given statement is incorrect.
(2a + 3b) (a – b)
= 2a (a – b) + 3b (a – b)
= 2a2 – 2ab + 3ab – 3b2
= 2a2 + ab – 3b2
The correct statement is
(2a + 3b) (a – b) = 2a2 + ab – 3b2
(14) (a + 4) (a + 2) = a2 + 8
The given statement is incorrect.
(a + 4) (a + 2)
= a (a + 2) + 4 (a + 2)
= a2 + 2a + 4a + 8
= a2 + 6a + 8
The correct statement is (a + 4) (a + 2) = a2 + 6a + 8

(15) (a – 4) (a – 2) = a2 – 8
The given statement is incorrect, (a – 4) (a – 2)
= a(a – 2) – 4(a – 2)
= a2 – 2a – 4a + 8
= a2 – 6a + 8
The correct statement is (a – 4) (a – 2) = a2 – 6a + 8

(16) $$\frac{3 x^{2}}{3 x^{2}}$$ = 0
The given statement is incorrect.
The correct statement is
$$\frac{3 x^{2}}{3 x^{2}}$$ = 1

(17) $$\frac{3 x^{2}+1}{3 x^{2}}$$ = 1 + 1 = 2
$$\frac{3 x^{2}+1}{3 x^{2}}=\frac{3 x^{2}}{3 x^{2}}+\frac{1}{3 x^{2}}=1+\frac{1}{3 x^{2}}$$
The given statement is incorrect.
The correct statement is
$$\frac{3 x^{2}+1}{3 x^{2}}=1+\frac{1}{3 x^{2}}$$

(18) $$\frac{3 x}{3 x+2}=\frac{1}{2}$$
The given statement is incorrect.
The correct statement is
$$\frac{3 x}{3 x+2}=\frac{3 x}{3 x+2}$$

(19) $$\frac{3}{4 x+3}=\frac{1}{4 x}$$
The given statement is incorrect.
The correct statement is $$\frac{3}{4 x+3}=\frac{3}{4 x+3}$$

(20) $$\frac{4 x+5}{4 x}$$ = 5
The given statement is incorrect.
$$\frac{4 x+5}{4 x}=\frac{4 x}{4 x}+\frac{5}{4 x}=1+\frac{5}{4 x}$$
The correct statement is
$$\frac{4 x+5}{4 x}=1+\frac{5}{4 x}$$

(21) = 7x
The given statement is incorrect.
$$\frac{7 \mathrm{x}+5}{5}=\frac{7 \mathrm{x}}{5}+\frac{5}{5}=\frac{7 \mathrm{x}}{5}+1$$
The correct statement is
$$\frac{7 x+5}{5}=\frac{7 x}{5}+1$$

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