## MP Board Class 8th Maths Solutions Chapter 14 Factorization Ex 14.4

Find and correct the errors in the following mathematical statements.

Question 1.

4(x – 5) = 4x – 5

Solution:

The given statement is incorrect.

The correct statement is 4(x – 5) = 4x – 20.

Question 2.

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

The given statement is incorrect.

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

Question 3.

2x + 3y = 5xy

Solution:

The given statement is incorrect.

The correct statement is 2x + 3y = 2x + 3y.

Question 4.

x + 2x + 3x = 5x

Solution:

The given statement is incorrect.

The correct statement is x + 2x + 3x = 6x.

Question 5.

5y + 2y + y – 7y = 0

Solution:

The given statement is incorrect.

The correct statement is 5y + 2y + y – 7y = y.

Question 6.

3x + 2x = 5x^{2}

The given statement is incorrect.

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

Question 7.

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

EH The given statement is incorrect.

The correct statement is (2x)^{2} + 4(2x) + 7

= 4x^{2} + 8x + 7.

Question 8.

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

EH The given statement is incorrect.

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

Question 9.

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

Solution:

The given statement is incorrect.

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

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

Question 10.

Substituting x = -3 in

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

gives (-3)^{2} + 5 (-3) + 4 = 9 + 2 + 4 = 15

(b) x^{2} – 5x + 4

gives (-3)^{2} – 5(-3) + 4 = 9 – 15 + 4 = -2

(c) x^{2} + 5x gives (-3)^{2} + 5 (-3) = -9 -15 = – 24

Solution:

(a) Incorrect statement

Substituting x = -3 in x^{2} + 5x + 4 gives

(-3)^{2} + 5(-3) + 4 = 9 – 15 + 4 = -2

(b) Incorrect statement

Substituting x = -3 in x^{2} – 5x + 4 gives

(-3)^{2} – 5(-3) + 4 = 9 + 15 + 4 = 28

(c) Incorrect statement

Substituting x = -3 in x^{2} + 5x gives

(-3)^{2} + 5(-3) = 9 – 15 = – 6

Question 11.

(y – 3)^{2} = y^{2} – 9

Solution:

The given statement is incorrect.

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

Question 12.

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

Solution:

The given statement is incorrect.

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

Question 13.

(2a + 3b)(a – b) = 2a^{2} – 3b^{2}

Solution:

The given statement is incorrect.

The correct statement is (2a + 3b)(a – b)

= 2a(a – b) + 3b(a – b)

= 2a^{2} – 2ab + 3ab – 3b^{2}

= 2a^{2} + ab – 3b^{2}

Question 14.

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

Solution:

The given statement is incorrect.

The correct statement is (a + 4) (a + 2)

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

= a^{2} + 2a + 4a + 8 = a^{2} + 6a + 8

Question 15.

(a – 4)(a – 2) = a^{2} – 8

Solution:

The given statement is incorrect.

The correct statement is (a – 4) (a – 2)

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

= a^{2} – 6a + 8

Question 16.

\(\frac{3 x^{2}}{3 x^{2}}\) = o

Solution:

The given statement is incorrect.

The correct statement is

\(\frac{3 x^{2}}{3 x^{2}}\) = 1

Question 17.

\(\frac{3 x^{2}+1}{3 x^{2}}\) = 1 + 1 = 2

Solution:

The given statement is incorrect.

The correct statement is

\(\frac{3 x^{2}+1}{3 x^{2}}=\frac{3 x^{2}}{3 x^{2}}+\frac{1}{3 x^{2}}=1+\frac{1}{3 x^{2}}\)

Question 18.

\(\frac{3 x}{3 x+2}=\frac{1}{2}\)

Solution:

The given statement is incorrect.

The correct statement is

\(\frac{3 x}{3 x+2}=\frac{3 x}{3 x+2}\)

Question 19.

\(\frac{3}{4 x+3}=\frac{1}{4 x}\)

Solution:

The given statement is incorrect.

The correct statement is \(\frac{3}{4 x+3}=\frac{3}{4 x+3}\)

Question 20.

\(\frac{4 x+5}{4 x}\) = 5

Solution:

The given statement is incorrect.

The correct statement is

\(\frac{4 x+5}{4 x}=\frac{4 x}{4 x}+\frac{5}{4 x}=1+\frac{5}{4 x}\)

Question 21.

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

Solution:

The given statement is incorrect.

The correct statement is

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

#### MP Board Class 8th Maths Solutions