Haryana State Board HBSE 8th Class Maths Solutions Chapter 14 Factorization Ex 14.4 Textbook Exercise Questions and Answers.
Haryana Board 8th Class Maths Solutions Chapter 14 Factorization Exercise 14.4
Find the correct the errors in the following matematical statements :
1. 4(x – 5) = 4x – 5
2. x(3x + 2) = 3x2 + 2
3. 2x + 3y = 5xy
4. x + 2x + 3x = 5x
5. 5y + 2y + y – 7y = 0
6. 3x + 2x = 5x2
7. (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7
8. (2x)2 + 5x = 4x + 5x = 9x
9. (3x + 2)2 = 3x2 + 6x + 4
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
11. (y – 3)2 = y2 – 9
12. (z + 5)2 = z2 + 25
13. (2a + 3b) (a – b) = 2a2 – 3b2
14. (a + 4) (a + 2) = a2 + 8
15. (a – 4) (a – 2) = a2 – 8
16. \(\frac{3 x^{2}}{3 x^{2}}\) = 0
17. \(\frac{3 x^{2}+1}{3 x^{2}}\) = 1 + 1 = 2
18. \(\frac{3 x}{3 x+2}\) = \(\frac{1}{2}\)
19. \(\frac{3}{4 x+3}\) = \(\frac{1}{4x}\)
20. \(\frac{4 x+5}{4 x}\) = 5
21. \(\frac{7 x+5}{5}\) = 7x.
Solution:
4(x – 5) = 4x – 5
L.H.S. = 4(x – 5)
= 4x – 20
Hence, 4(x – 5) = 4x – 20
2. x(3x + 2) = 3x2 + 2
L.H.S. = x(3x + 2)
= 3x2 + 2x .
Hence, x(3x + 2) = 3x2 + 2x
3. 2x + 3y = 5x
L.H.S. = 2x + 3y
Hence, 2x + 3y = 2x + 3y or 3y + 2x
4. x + 2x + 3x = 5x
L.H.S. = x + 2x + 3x
= 6x
Hence, x + 2x + 3x = 6x
5. 5y + 2y + y – 7y = 0
L.H.S. = 5y + 2y + y – 7y
= 7y – 7y + y
= y
Hence, 5y + 2y + y – 7y = y
6. 3x + 2x = 5x2
L.H.S. = 3x + 2x = 5x
Hence, 3x + 2x = 5x
7. (2x)2 + 4 (2x) + 7 = 2x2 + 8x + 7
L.H.S: = (2x)2 + 4 (2x) + 7
= 4x2 + 8x + 7
Hence,
(2x)2 + 4(2x) + 7 = 4x2 + 8x + 7
8. (2x)2 + (5x) = 4x + 5x = 9x
L.H.S. = (2x)2 + (5x)
= 4x2 + 5x
Hence, (2x)2 + (5x) = 4x2 + 5x
9. (3x + 2)2 = 3x2 + 6x + 4
L.H.S. = (3x + 2)2
= (3x)2 + 2 × 3x × 2 + (2)2
[∵ (a + b)2 = a2 + 2ab + b2]
= 9x2 + 12x + 4
Hence, (3x + 2)2 = 9x2 + 12x + 4
10 (a). If x = -3
x2 + 5x + 4 gives (-3)2 + 5 (-3) + 4
= 9 + 2 + 4 = 15
L.H.S. = x2 + 5x + 4
= (-3)2 + 5 × (-3) + 4
= 9 + (-15) + 4
= 13 – 15 = -2
Hence, x2 + 5x + 4 = -2
(b) If x = -3
x2 – 5x + 4 = (-3)2 + 5 (-3) + 4
= 9 + 15 + 4 = 28
(c) If x = -3
x2 + 5x = =(-3)2 + 5(-3)
= 9 + (-15)
= 9 – 15 = -6
11. (y – 3)2 = y2 – 9
= y2 – 2 × y × 3 + (3)2
[∵ (a – b)2 = a2 – 2ab + b2]
= y2 – 6y + 9
Hence, (y – 3)2 = y2 – 6y + 9
12. (z + 5)2 = z2 + 25
L.H.S. = (z + 5)2
= (z)2 + 2 × z × 5 + (5)2
= z2 + 10z + 25
Hence, (z + 5)2 = z2 + 10z + 25
13. (2a + 3b) (a – b) = 2a2 – 3b2
L.H.S. = (2a + 3b) (a – b)
= 2a2 – 2ab + 3ab – 3b2
= 2a2 – ab – 3b2
Hence, (2a + 3b) (a – b) = 2a2 + ab – 3b2.
14. (a + 4)(a + 2) = a2 + 8
(a + 4)(a + 2) = a2 + 8
L.H.S. = (a + 4)(a + 2)
= a2 + 2a + 4a + 8
= a2 + 6a + 8
Hence, (a + 4) (a + 2) = a2 + 6a + 8
15. (a – 4)(a – 2) = a2 – 8
L.H.S. = (a – 4)(a – 2)
= a2 – 2a – 4a + 8
= a2 – 6a + 8
Hence, (a – 4) (a – 2) = a2 – 6a + 8.
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