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.

Answer:

(1) 4(x – 5) = 4x – 5

The given statement is incorrect.

The correct statement is

4(x – 5) = 4x – 20

(2) x (3x + 2) = 3x^{2} + 2

The given statement is incorrect.

The correct statement is x (3x + 2) = 3x^{2} + 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 = 5x^{2}

This is an incorrect statement.

The correct statement is 3x + 2x = 5x

(7) (2x)^{2} + 4(2x) + 7 = 2x^{2} + 8x + 7

This given statement is incorrect.

The correct statement is

(2x)^{2} + 4 (2x) + 7 = 4x^{2} + 8x + 7

(8) (2x)^{2} + 5x = 4x + 5x = 9x^{2}

The given statement is incorrect.

The correct statement is (2x)^{2} + 5x = 4x^{2} + 5x

(9) (3x + 2)^{2} = 3x^{2} + 6x + 4

The given statement is incorrect.

The correct statement is

(3x + 2)^{2} = (3x)^{2} + 2 × 3x × 2 + (2)^{2}

(3x + 2)^{2} = 9x^{2} + 12x + 4

(10) Substituting x = – 3 in

(a) x^{2} + 5x + 4

= (- 3)^{2} + 5 (-3) + 4

= 9 + 2 + 4

= 15

The given statement is incorrect.

The correct statement is x^{2} + 5x + 4

= (-3)^{2} + 5 (- 3) + 4

= 9 – 15 + 4

= 13 – 15 = – 2

∴ x^{2} + 5x + 4 = -2 at x = – 3

(b) x^{2} – 5x + 4

= (-3)^{2} – 5 (-3) + 4

= 9 – 15 + 4 = -2

The given statement is incorrect.

The correct statement is

x^{2} – 5x + 4

= (-3)^{2} – 5 (-3) + 4

= 9 + 15 +4 = 28

(c) x^{2} + 5x = (-3)^{2} + 5 (-3)

= – 9 – 15 = – 24

The given statement is incorrect.

The correct statement is

x^{2} + 5x

= (-3)^{2} + 5(—3)

= 9 – 15 = -6

(11) (y – 3)^{2} = y^{2} – 9

The given statement is incorrect. (y-3)^{2}

= y^{2} – 2 (y) (3) + 3^{2}

= y^{2} – 6y + 9

The correct statement is (y – 3)^{2} = y^{2} – 6y + 9

(12) (z + 5)^{2} = z^{2} + 25

The given statement is incorrect.

(z + 5)^{2} = z^{2} + 2 × z × 5 + 5^{2}

= z^{2} + 10z + 25

The correct statement is (z + 5)^{2} = z^{2} + 10z + 25

(13) (2a + 3b) (a – b) = 2a^{2} – 3b^{2}

The given statement is incorrect.

(2a + 3b) (a – b)

= 2a (a – b) + 3b (a – b)

= 2a^{2} – 2ab + 3ab – 3b^{2}

= 2a^{2} + ab – 3b^{2}

The correct statement is

(2a + 3b) (a – b) = 2a^{2} + ab – 3b^{2}

(14) (a + 4) (a + 2) = a^{2} + 8

The given statement is incorrect.

(a + 4) (a + 2)

= a (a + 2) + 4 (a + 2)

= a^{2} + 2a + 4a + 8

= a^{2} + 6a + 8

The correct statement is (a + 4) (a + 2) = a^{2} + 6a + 8

(15) (a – 4) (a – 2) = a^{2} – 8

The given statement is incorrect, (a – 4) (a – 2)

= a(a – 2) – 4(a – 2)

= a^{2} – 2a – 4a + 8

= a^{2} – 6a + 8

The correct statement is (a – 4) (a – 2) = a^{2} – 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

\(\frac{7 x+5}{5}=\frac{7 x}{5}+1\)