RS Aggarwal solution class 8 chapter 7 Factorisation Exercise 7E

Exercise 7E

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Q1 | Ex-7E | Class 8 | RS AGGARWAL | Chapter 7 | Factorisation | myhelper

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Question 1:

Tick (✓) the correct answer:
(7a² − 63b²) = ?
(a) (7a − 9b)(9a + 7b)
(b) (7a − 9b)(7a + 9b)
(c) 9(a − 3b)(a + 3b)
(d) 7(a − 3b)(a + 3b)

Answer 1:

(d) 7(a − 3b)(a + 3b)

$$\begin{gathered} (7a^2 -63b^2)=7(a^{2 }-9b^2) \\ =7(a -3b)(a+3b) \end{gathered}$$

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Question 2:

Tick (✓) the correct answer:
(2x − 32x³) = ?
(a) 2(x − 4)(x + 4)
(b) 2x(1 − 2x)²
(c) 2x(1 + 2x)²
(d) 2x(1 − 4x)(1 + 4x)

Answer 2:

(d) 2x(1 − 4x)(1 + 4x)

$$\begin{gathered} (2x-32x^3) \\ =2x(1-16x^2) \\ =2x(1-4x)(1+4x) \end{gathered}$$

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Question 3:

Tick (✓) the correct answer:
x³ − 144x = ?
(a) x(x − 12)²
(b) x(x + 12)²
(c) x(x − 12)(x + 12)
(d) none of these

Answer 3:

(c) x(x − 12)(x + 12)

$$\begin{gathered} x^3 - 144x \\ =x(x^2 -144) \\ =x(x-12)(x+12) \end{gathered}$$

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Question 4:

Tick (✓) the correct answer:
(2 − 50x²) = ?
(a) 2(1 − 5x)²
(b) 2(1 + 5x)²
(c) (2 − 5x)(2 + 5x)
(d) 2(1 − 5x)(1 + 5x)

Answer 4:

(d) 2(1 − 5x)(1 + 5x)

$$\begin{gathered} 2-50x^{2 } \\ =2(1-25x^2) \\ =2(1-5x)(1+5x) \end{gathered}$$

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Question 5:

Tick (✓) the correct answer:
a² + bc + ab + ac = ?
(a) (a + b)(a + c)
(b) (a + b)(b + c)
(c) (b + c)(c + a)
(d) a(a + b + c)

Answer 5:

(a) (a + b)(a + c)

$$\begin{gathered} a^2+bc +ab +ac \\ =a^2+ab+bc +ac \\ =a(a+b)+c(a+b) \\ =(a+c)(a+b) \end{gathered}$$

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Question 6:

Tick (✓) the correct answer:
pq² + q(p − 1) − 1 = ?
(a) (pq + 1)(q − 1)
(b) p(q + 1)(q − 1)
(c) q(p − 1)(q + 1)
(d) (pq − 1) (q + 1)

Answer 6:

(d) (pq − 1) (q + 1)

$$\begin{gathered} p{q}^2+q(p-1)-1 \\ =p{q}^2+qp-q-1 \\ =pq(q+1)-1(q+1) \\ =(pq-1)(q+1) \end{gathered}$$

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Question 7:

Tick (✓) the correct answer:
ab − mn + an − bm = ?
(a) (a − b)(m − n)
(b) (a − m)(b + n)
(c) (a − n)(m + b)
(d) (m − a)(n − b)

Answer 7:

(b) (a − m)(b + n)

$$\begin{gathered} ab-mn+an-bm \\ =ab+an-mn-bm \\ =a(b+n)-m(n+b) \\ =(a-m)(b+n) \end{gathered}$$

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Question 8:

Tick (✓) the correct answer:
ab − a − b + 1 = ?
(a) (a − 1)(b − 1)
(b) (1 − a)(1 − b)
(c) (a − 1)(1 − b)
(d) (1 − a)(b − 1)

Answer 8:

(a) (a − 1)(b − 1)

$$\begin{gathered} ab-a-b+1 \\ =a(b-1)-1(b-1) \\ =(a-1)(b-1) \end{gathered}$$

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Question 9:

Tick (✓) the correct answer:
x² − xz + xy − yz = ?
(a) (x − y)(x + z)
(b) (x − y)(x − z)
(c) (x + y)(x − z)
(d) (x − y)(z − x)

Answer 9:

(c) (x + y)(x − z)

$$\begin{gathered} x^2-xz+xy-yz \\ =x(x-z)+y(x-z) \\ =(x+y) (x-z) \end{gathered}$$

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Question 10:

Tick (✓) the correct answer:
(12m² − 27) = ?
(a) (2m − 3)(3m − 9)
(b) 3(2m − 9)(3m − 1)
(c) 3(2m − 3)(2m + 3)
(d) none of these

Answer 10:

(c) 3(2m − 3)(2m + 3)

$$\begin{gathered} 12m^2-27 \\ =3(4m^2-9) \\ =3 (2m-3)(2m+3) \end{gathered}$$

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Question 11:

Tick (✓) the correct answer:
x³ − x = ?
(a) x(x² − x)
(b) x(x − x²)
(c) x(1 + x)(1 − x)
(d) x(x + 1)(x − 1)

Answer 11:

(d) x(x + 1)(x − 1)

$$\begin{gathered} x^3-x \\ =x( x^2-1) \\ =x(x-1)(x+1) \end{gathered}$$

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Question 12:

Tick (✓) the correct answer:
1 − 2ab − (a² + b²) = ?
(a) (1 + a − b)(1 + a + b)
(b) (1 + a + b)(1 − a + b)
(c) (1 + a + b)(1 − a − b)
(d) (1 + a − b)(1 − a + b)

Answer 12:

(c) (1 + a + b)(1 − a − b)

$$\begin{gathered} 1-2ab-(a^{2 }+b^2) \\ =1-2ab -a^2-b^2 \\ =1-(2ab +a^2+b^2) \\ =1-(a+b{)}^2 \\ =(1-a-b\left)\right(1+a+b) \end{gathered}$$

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Question 13:

Tick (✓) the correct answer:
x² + 6x + 8 = ?
(a) (x + 3)(x + 5)
(b) (x + 3)(x + 4)
(c) (x + 2)(x + 4)
(d) (x + 1)(x + 8)

Answer 13:

(c) (x + 2)(x + 4)

$$\begin{gathered} x^2+6x+8 \\ =x^2+4x+2x+8 \\ =x(x+4)+2(x+4) \\ =(x+2)(x+4) \end{gathered}$$

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Question 14:

Tick (✓) the correct answer:
x² + 4x − 21 = ?
(a) (x − 7)(x + 3)
(b) (x + 7)(x − 3)
(c) (x − 7)(x − 3)
(d) (x + 7)(x + 3)

Answer 14:

(b) (x + 7)(x − 3)

$$\begin{gathered} x^2+4x-21 \\ =x^2+7x-3x-21 \\ =x(x+7)-3(x+7) \\ =(x-3)(x+7) \end{gathered}$$

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Question 15:

Tick (✓) the correct answer:
y² + 2y − 3 = ?
(a) (y − 1)(y + 3)
(b) (y + 1)(y − 3)
(c) (y − 1)(y − 3)
(d) (y + 2)(y − 3)

Answer 15:

(a) (y − 1)(y + 3)

$$\begin{gathered} y^2+2y-3 \\ =y^2+3y-y-3 \\ =y(y+3)-1(y+3) \\ =(y-1)(y+3) \end{gathered}$$

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Question 16:

Tick (✓) the correct answer:
40 + 3x − x² = ?
(a) (x + 5)(x − 8)
(b) (5 − x)(8 + x)
(c) (5 + x)(8 − x)
(d) (5 − x)(8 − x)

Answer 16:

(c) (5 + x)(8 − x)

$$\begin{gathered} 40+3x-x^2 \\ =40+8x-5x-x^2 \\ =8(5+x)-x(5+x) \\ =(8-x)(x+5) \end{gathered}$$

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Question 17:

Tick (✓) the correct answer:
2x² + 5x + 3 = ?
(a) (x + 3)(2x + 1)
(b) (x + 1)(2x + 3)
(c) (2x + 5)(x − 3)
(d) none of these

Answer 17:

(b) (x + 1)(2x + 3)

$$\begin{gathered} 2x^2+5x+3 \\ =2x^2+2x+3x+3 \\ =2x(x+1) +3(x+1) \\ =(2x +3) (x+1) \end{gathered}$$

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Question 18:

Tick (✓) the correct answer:
6a² − 13a + 6 = ?
(a) (2a + 3)(3a − 2)
(b) (2a − 3)(3a + 2)
(c) (3a − 2)(2a − 3)
(d) (3a + 1)(2a − 3)

Answer 18:

(c) (3a − 2)(2a − 3)

$$\begin{gathered} 6a^2-13a+6 \\ =6a^2-9a-4a+6 \\ =3a(2a-3)-2(2a-3) \\ =(3a-2)(2a-3) \end{gathered}$$

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Question 19:

Tick (✓) the correct answer:
4z² − 8z + 3 = ?
(a) (2z − 1)(2z − 3)
(b) (2z + 1)(3 − 2z)
(c) (2z + 3)(3z − 1)
(c) (z − 1)(4z − 3)

Answer 19:

(a) (2z − 1)(2z − 3)

$$\begin{gathered} 4z^2-8z+3 \\ =4z^2-6z-2z+3 \\ =2z(2z-3)-1(2z-3) \\ =(2z-1)(2z-3) \end{gathered}$$

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Question 20:

Tick (✓) the correct answer:
3 + 23y − 8y² = ?
(a) (1 − 8y)(3 + y)
(b) (1 + 8y)(3 − y)
(c) (1 − 8y)(y − 3)
(d) (8y − 1)(y + 3)

Answer 20:

(b) (1 + 8y)(3 − y)

$$\begin{gathered} 3+23y-8y^2 \\ =3+24y-y-8y^2 \\ =3(1+8y)-y(1+8y) \\ =(3-y)(1+8y) \end{gathered}$$