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

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.

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

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.

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

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

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

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

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

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