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) = 3x² + 2
The given statement is incorrect.
The correct statement is x(3x + 2) = 3x² + 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 = 5x²
The given statement is incorrect.
The correct statement is 3x + 2x = 5x.

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

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

Question 9.
(3x + 2)² = 3x² + 6x + 4
Solution:
The given statement is incorrect.
The correct statement is (3x + 2)²
= (3x)² + 2(3x)(2) + 2² = 9x² + 12x + 4.

Question 10.
Substituting x = -3 in
(a) x² + 5x + 4
gives (-3)² + 5 (-3) + 4 = 9 + 2 + 4 = 15
(b) x² – 5x + 4
gives (-3)² – 5(-3) + 4 = 9 – 15 + 4 = -2
(c) x² + 5x gives (-3)² + 5 (-3) = -9 -15 = – 24
Solution:
(a) Incorrect statement
Substituting x = -3 in x² + 5x + 4 gives
(-3)² + 5(-3) + 4 = 9 – 15 + 4 = -2
(b) Incorrect statement
Substituting x = -3 in x² – 5x + 4 gives
(-3)² – 5(-3) + 4 = 9 + 15 + 4 = 28
(c) Incorrect statement
Substituting x = -3 in x² + 5x gives
(-3)² + 5(-3) = 9 – 15 = – 6

Question 11.
(y – 3)² = y² – 9
Solution:
The given statement is incorrect.
The correct statement is (y – 3)² = y² – 6y + 9

Question 12.
(z + 5)² = z² + 25
Solution:
The given statement is incorrect.
The correct statement is (z + 5)² = z² + 10z + 25

Question 13.
(2a + 3b)(a – b) = 2a² – 3b²
Solution:
The given statement is incorrect.
The correct statement is (2a + 3b)(a – b)
= 2a(a – b) + 3b(a – b)
= 2a² – 2ab + 3ab – 3b²
= 2a² + ab – 3b²

Question 14.
(a + 4)(a + 2) = a² + 8
Solution:
The given statement is incorrect.
The correct statement is (a + 4) (a + 2)
= a(a + 2) + 4 (a + 2)
= a² + 2a + 4a + 8 = a² + 6a + 8

Question 15.
(a – 4)(a – 2) = a² – 8
Solution:
The given statement is incorrect.
The correct statement is (a – 4) (a – 2)
= a(a – 2) – 4(a – 2) = a² – 2a – 4a + 8
= a² – 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
\(\frac{7 x+5}{5}=\frac{7 x}{5}+\frac{5}{5}=\frac{7 x}{5}+1\)