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Factorisation : Exercise 14.4 (Mathematics NCERT Class 8th)


Find and correct the errors in the following mathematical statements.
Q.1. 4(x - 5) = 4x - 5
Sol. Given, 4(x - 5) = 4x - 5
LHS = 4(x - 5)
= 4x - 20
≠RHS
Correct statement: 4(x - 5) = 4x - 20

Q.2. x(3x + 2) = 3{x^2} + 2
Sol. Given, x(3x + 2) = 3{x^2} + 2
LHS = x(3x + 2)
= 3{x^2} + 2x
≠RHS
Correct statement: x(3x + 2) = 3{x^2} + 2x

Q.3. 2x + 3y = 5xy
Sol. Given, 2x + 3y = 5xy
LHS = 2x + 3y
≠RHS
Correct statement: 2x + 3y = 2x + 3y

Q.4. x + 2x + 3x = 5x
Sol. Given, x + 2x + 3x = 5x
LHS = x + 2x + 3x
= 6x
≠RHS
Correct statement: x + 2x + 3x = 6x

Q.5 5y + 2y + y - 7y = 0
Sol. Given, 5y + 2y + y - 7y = 0
LHS = 5y + 2y + y - 7y
= 8y - 7y
= y
≠RHS
Correct statement: 5y + 2y + y - 7y = y

Q.6 3x + 2x = 5{x^2}
Sol. Given, 3x + 2x = 5{x^2}
LHS = 3x + 2x
= 5x
≠RHS
Correct statement: 3x + 2x = 5x

Q.7 {(2x)^2} + 4(2x) + 7 = 2{x^2} + 8x + 7
Sol. Given, {(2x)^2} + 4(2x) + 7 = 2{x^2} + 8x + 7
LHS = {(2x)^2} + 4(2x) + 7
= 4{x^2} + 8x + 7
≠RHS
Correct statement: {(2x)^2} + 4(2x) + 7 = 4{x^2} + 8x + 7

Q.8 {(2x)^2} + 5x = 4x + 5x = 9x
Sol. Given, {(2x)^2} + 5x = 4x + 5x = 9x
LHS = {(2x)^2} + 5x
= 4{x^2} + 5x
≠RHS
Correct statement: {(2x)^2} + 5x = 4{x^2} + 5x

Q.9 {(3x + 2)^2} = 3{x^2} + 6x + 4
Sol. Given, {(3x + 2)^2} = 3{x^2} + 6x + 4
LHS = {(3x + 2)^2}
= 9{x^2} + 12x + 4
≠RHS
Correct statement: {(3x + 2)^2} = 9{x^2} + 12x + 4

Q.10 Substituting x = - 3 in
(a) {x^2} + 5x + 4gives {( - 3)^2} + 5( - 3) + 4 = 9 + 2 + 4 = 15
(b) {x^2} - 5x + 4gives {( - 3)^2} - 5( - 3) + 4 = 9 - 15 + 4 = - 2
(c) {x^2} + 5xgives {( - 3)^2} + 5( - 3) = - 9 - 15 = - 24
Sol. (a) {x^2} + 5x + 4gives {( - 3)^2} + 5( - 3) + 4 = 9 + 2 + 4 = 15
LHS = {x^2} + 5x + 4
Substituting , we get,
= {( - 3)^2} + 5( - 3) + 4
= 9 - 15 + 4
=  - 2
≠RHS
Correct statement: {x^2} + 5x + 4gives {( - 3)^2} + 5( - 3) + 4 = 9 - 15 + 4 = - 2

(b) {x^2} - 5x + 4gives {( - 3)^2} - 5( - 3) + 4 = 9 - 15 + 4 = - 2
LHS = {x^2} - 5x + 4
Substituting , we get,
= {( - 3)^2} - 5( - 3) + 4
= 9 + 15 + 4
= 28
≠RHS
Correct statement: {x^2} - 5x + 4gives {( - 3)^2} - 5( - 3) + 4 = 9 + 15 + 4 = 28

(c) {x^2} + 5xgives {( - 3)^2} + 5( - 3) = - 9 - 15 = - 24
LHS = {x^2} + 5x
Substituting , we get,
= {( - 3)^2} + 5( - 3)
= 9 - 15
=  - 6
≠RHS
Correct statement: {x^2} + 5xgives {( - 3)^2} + 5( - 3) = 9 - 15 = - 6

Q.11 {(y - 3)^2} = {y^2} - 9
Sol. LHS = {(y - 3)^2}
= {y^2} - 6y + 9
≠RHS
Correct statement: {(y - 3)^2} = {y^2} - 6y + 9

Q.12 {(z + 5)^2} = {z^2} + 25
Sol. LHS = {(z + 5)^2}
= {z^2} + 10z + 25
≠RHS
Correct statement: {(y - 3)^2} = {y^2} - 6y + 9

Q.13 (2a + 3b)(a - b) = 2{a^2} - 3{b^2}
Sol. LHS = (2a + 3b)(a - b)
= 2{a^2} - 2ab + 3ab - 3{b^2}
= 2{a^2} + ab - 3{b^2}
≠RHS
Correct statement: (2a + 3b)(a - b) = 2{a^2} + ab - 3{b^2}

Q.14 (a + 4)(a + 2) = {a^2} + 8
Sol. LHS = (a + 4)(a + 2)
= {a^2} + 2a + 4a + 8
= {a^2} + 6a + 8
≠RHS
Correct statement: (a + 4)(a + 2) = {a^2} + 6a + 8

Q.15 (a - 4)(a - 2) = {a^2} - 8
Sol. LHS = (a - 4)(a - 2)
= {a^2} - 2a - 4a + 8
= {a^2} - 6a + 8
≠RHS
Correct statement: (a - 4)(a - 2) = {a^2} - 6a + 8

Q.16 {{3{x^2}} \over {3{x^2}}} = 0
Sol. LHS = {{3{x^2}} \over {3{x^2}}}
= 1
≠RHS
Correct statement: {{3{x^2}} \over {3{x^2}}} = 1

Q.17 {{3{x^2} + 1} \over {3{x^2}}} = 1 + 1 = 2
Sol. LHS = {{3{x^2} + 1} \over {3{x^2}}}
= {{3{x^2}} \over {3{x^2}}} + {1 \over {3{x^2}}}
= 1 + {1 \over {3{x^2}}}
≠RHS
Correct statement: {{3{x^2} + 1} \over {3{x^2}}} = 1 + {1 \over {3{x^2}}}

Q.18 {{3x} \over {3x + 2}} = {1 \over 2}
Sol. LHS = {{3x} \over {3x + 2}}
≠RHS
Correct statement: {{3x} \over {3x + 2}} = {{3x} \over {3x + 2}}

Q.19 {3 \over {4x + 3}} = {1 \over {4x}}
Sol. LHS = {3 \over {4x + 3}}
≠RHS
Correct statement: {3 \over {4x + 3}} = {3 \over {4x + 3}}

Q.20 {{4x + 5} \over {4x}} = 5
Sol. LHS = {{4x + 5} \over {4x}}
= {{4x} \over {4x}} + {5 \over {4x}}
= 1 + {5 \over {4x}}
≠RHS
Correct statement: {{4x + 5} \over {4x}} = 1 + {5 \over {4x}}

Q.21 {{7x + 5} \over 5} = 7x
Sol. LHS = {{7x + 5} \over 5}
= {{7x} \over 5} + {5 \over 5}
= {{7x} \over 5} + 1
≠RHS
Correct statement: {{7x + 5} \over 5} = {{7x} \over 5} + 1



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