**Selina Concise Class 7 Math Chapter 11 Fundamental Concepts Exercise 11F Solution**

EXERCISE 11F

Enclose the given terms in brackets as required:

(1) x – y – z = x – (y + z)

(2) x^{2} – xy^{2} – 2xy – y^{2} = x^{2} – (xy^{2} + 2xy + y^{2})

(3) 4a – 9 + 2b – 6 = 4a – (9 – 2b + 6)

(4) x^{2} – y^{2} + z^{2} + 3x – 2y = x^{2} – (y^{2} – z^{2} – 3x + 2y)

(5) – 2a^{2} + 4ab – 6a^{2}b^{2} + 8ab^{2} = – 2a (a – 2b + 3ab^{2} + 4b^{2})

Simplify:

(6) 2x – (x + 2y – z)

= 2x – x – 2y + z

= x – 2y + z

(7) p + q – (p – q) + (2p – 3q)

= p + q – p + q + 2p – 3q

= 2q + 2p – 3q

= 2p – q

(8) 9x – (- 4x + 5)

= 9x + 4x – 5

= 13x – 5

(9) 6a – (- 5a – 8b) + (3a + b)

= 6a + 5a + 8b + 3a + b

= 14a + 9b

(10) (p – 2q) – (3q – r)

= p – 2q – 3q + r

= p – 5q + r

(11) 9a (2b – 3a + 7c)

= 18ab – 27a^{2} + 63ac

(12) – 5m (- 2m + 3n – 7p)

= 10m^{2} – 15mn + 35pm

(13) – 2x (x + y) + x^{2}

= – 2x^{2} – 2xy + x^{2}

= – x^{2} – 2xy

(15) 8 (2a + 3b – c) – 10 (a + 2b + 3c)

= 16a + 24b – 8c – 10a – 20b – 30c

= 6a + 4b – 38c

(17) 5x (2x + 3y) – 2x (x – 9y)

= 10x^{2} + 15xy – 2x^{2} + 18xy

= 8x^{2} + 33xy

(18) a + (b + c – d)

= a + b + c – d

(19) 5 – 8x – 6 – x

= – 9x – 1

(20) 2a + {b – (a – b)}

= 2a + {b – a + b}

= 2a + b – a + b

= a + 2b

(21) 3x + [4x – (6x – 3)]

= 3x + [4x – 6x + 3]

= 3x + [- 2x + 3]

= 3x – 2x + 3

= x + 3

(22) 5b – {6a + (8 – b – a)}

= 5b – {6a + 8 – b – a}

= 5b – 6a – 8 + b + a

= 6b – 5a – 8

(23) 2x – [5y – (3x – y) + x]

= 2x –[5y – 3x + y + x]

= 2x – [6y – 2x]

= 2x – 6y + 2x

= 4x – 6y

(24) 6a – 3 (a + b – 2)

= 6a – 3a – 3b + 6

= 3a – 3b + 6

(25) 8 [m + 2n – p – 7(2m – n + 3p)]

= 8 [m + 2n – p – 14m + 7n – 21p]

= 8m + 16n – 8p – 112m + 56n – 168p

= – 104m + 72n – 176p

(26) {9 – (4p – 6q)} – {3q – (5p – 10)}

= {9 – 4p + 6q} – {3q – 5p + 10}

= 9 – 4p + 6q – 3q + 5p – 10

= p + 3q – 1

(27) 2 [a – 3 {a + 5 (a – 2) + 7}]

= 2 [a – 3 {a + 5a – 10 + 7}]

= 2 [a – 3{6a – 3}]

= 2 [a – 18a + 9]

= 2 [ – 17a + 9]

= – 34a + 18

(28) 5a – [6a – {9a – (10a – (4a – 3a))}]

= 5a – [6a – 9a – (10a – a)}]

= 5a – [6a – 9a + 9a]

= 5a – [6a]

= – a

(29) 9x + 5 – [4x – {3x – 2 (4x – 3)}]

= 9x + 5 – [4x – {3x – 8x + 6}]

= 9x + 5 – [4x – {- 5x + 6}]

= 9x + 5 – [4x + 5x – 6]

= 9x + 5 – [9x – 6]

= 9x + 5 – 9x + 6

= 11

(30) (x + y – z) x + (z + x – y) y – (x + y – z) z

= x^{2} + xy – xz + zy + xy – y^{2} – xz – yz + z^{2}

= x^{2} – y^{2} + z^{2} + 2xy – 2xz

(31) – 1 [a – 3 {b – 4 (a – b – 8) + 4a} + 10]

= – 1[a – 3 {b – 4a + 4b + 32 + 4a} + 10]

= – 1[a – 3 {5b + 32} + 10]

= – 1 [a – 15b – 96 + 10]

= – 1 [a – 15b – 86]

= – a + 15b + 86

(32) p^{2} – [x^{2} – {x^{2} – (q^{2} – (x^{2} – q^{2}) – 2y^{2}}]

= p^{2} – [x^{2} – {x^{2} – (q^{2} – x^{2} – q^{2} – 2y^{2}]

= p^{2} – [x^{2} – {x^{2} – q^{2} + x^{2} – q^{2} – 2y^{2}]

= p^{2} – [x^{2} – x^{2} + q^{2} – x^{2} + q^{2} + 2y^{2}]

= p^{2} – [2q^{2} – x^{2} + 2y^{2}]

= p^{2} – 2q^{2} + x^{2} – 2y^{2}

(33) 10 – [4a – {7 – (a – 5)} – {5a – (1 + a)}]

= 10 – [4a – {7 – a + 5} – {5a – 1 – a}]

= 10 – [4a – {12 – a} – {4a – 1}]

= 10 – [4a – 12 + a – 4a + 1]

= 10 – [a – 11]

= 10 – a + 11

= 21 – a

(34) 7a – [8a – {11a – (12a – (6a – 5a))}]

= 7a – [8a – {11a – (12a – 6a + 5a)}]

= 7a – [8a – {11a – (12a – a)}]

= 7a – [8a – {11a – 11a}]

= 7a – [8a – 11a + 11a]

= 7a – 8a

= – a

(35) 8x – [4y – {4x + (2x – (2y – 2x))}]

= 8x – [4y – {4x + (2x – 2y + 2x)}]

= 8x – [4y – {4x + 4x – 2y}]

= 8x – [4y – 8x + 2y]

= 8x – [6y – 8x]

= 8x – 6y + 8x

= 16x – 6y

(36) x – {3y – (4z – 3x) + 2z – (5y – 7x)}

= x – {3y – 4z + 3x + 2z – 5y + 7x}

= x – {- 2y – 2z + 10x}

= x + 2y + 2z – 10x

= – 9x + 2y + 2z

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