KSEEB Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.4
KSEEB Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.4
KSEEB Solutions for Class 8 Maths Chapter 14 Factorization Ex 14.4
Find and correct the errors in the following mathematical statements.
Question 1.
4(x – 5) = 4x – 5
Solution:
4(x – 5) = 4x – 5
L.H.S. = 4(x – 5) = 4x – 20
4x – 20 ≠ 4x – 5
∴ 4(x – 5) = 4x – 20
Question 2.
x(3x + 2) = 3x2 + 2
Solution:
x(3x + 2) = 3x2 + 2
L.H.S. = x(3x + 2) = 3x2 + 2x
3x2 + 2x ≠ 3x2 + 2
∴ Correct statement x(3x + 2) = 3x2 + 2x
Question 3.
2x + 3y = 5xy
Solution:
2x + 3y = 5xy
L.H.S. = 2x + 3y = 2x + 3y
Incorrect statement
2x + 3y ≠ 5xy
∴ Correct statement 2x + 3y = 2x + 3y
Question 4.
x + 2x + 3x = 5x
Solution:
x + 2x + 3x = 5x
L.H.S. = x + 2x + 3x = 6x
6x ≠ 5x
Correct statement x + 2x + 3x = 6x
Question 5.
5y + 2y + y – 7y = 0
Solution:
5y + 2y + y – 7y = 0
L.H.S. = 5y + 2y + y – 7y
= 8y – 7y
= y
y ≠ 0
∴ Correct statement 5y + 2y + y – 7y = y
Question 6.
3x + 2x = 5x2
Solution:
3x + 2x = 5x2
L.H.S. = 3x + 2x = 5x
5x ≠ 5x2
∴ Correct statement 3x + 2x = 5x
Question 7.
(2x)2 + 4(2x) + 7 = 2x2 + 8x + 7
Solution:
(2x)2 + 4(2x) + 7 = 2x2 + 8x + 7
L.H.S. = (2x)2 + 4(2x) + 7
= 4x2 + 8x + 7
4x2 + 8x + 7 ≠ 2x2 + 8x + 7
Correct statement (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7
Question 8.
(2x)2 + 5x = 4x + 5x = 9x
Solution:
(2x)2 + 5x = 4x + 5x = 9x
L.H.S. = (2x)2 + 5x = 4x2 + 5x
4x2 + 5x ≠ 4x + 5x = 9x
∴ Correct statement (2x)2 + 5x = 4x2 + 5x
Question 9.
(3x + 2)2 = 3x2 + 6x + 4
Solution:
(3x + 2)2 = 3x2 + 6x + 4
L.H.S. = (3x + 2)2
= (3x)2 + 2(3x) (2) + (2)2
= 9x2 + 12x + 4
∴ Correct statement (3x + 2)2 = 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) x2 + 5x + 4
When x = -3
x2 + 5x + 4
= (-3)2 + 5(-3) + 4
= 9 – 15 + 4
= 13 – 15
= -2
It gives -2
(b) x2 – 5x + 4
When x = -3
x2 – 5x + 4
= (-3)2 – 5(-3) + 4
= 9 + 15 + 4
= 28
It gives 28
(c) x2 + 5x
When x = -3
x2 + 5x
= (-3)2 + 5(-3)
= 9 – 15
= -6
It gives -6
Question 11.
(y – 3)2 = y2 – 9
Solution:
(y – 3)2
= (y)2 – 2(y) (3) + (3)2
= y2 – 6y + 9
Question 12.
[z + 5]2 = z2 + 25
Solution:
(z + 5)2
= z2 + 2(z) (5) + (5)2
= z2 + 10z + 25
Question 13.
(2a + 3b) (a – b) = 2a2 – 3b2
Solution:
(2a + 3) (a – b)
= 2a × a – 2a × b + 3a – 3b
= 2a2 – 2ab + 3a – 3b
Question 14.
(a + 4) (a + 2) = a2 + 8
Solution:
(a + 4) (a + 2)
= a × a + 2a + 4a + 4 × 2
= a2 + 6a + 8
Question 15.
(a – 4) (a – 2) = a2 – 8
Solution:
(a – 4) (a – 2)
= a(a – 2) – 4(a – 2)
= a2 – 2a – 4a + 8
= a2 – 6a + 8
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