PRACTISE QUESTIONS (Algebraic expressions and Identities) Q.1 Simplify the following expressions: (i) (x + y + z)(x + y – z) (ii) x2 (x – 3y2 ) – xy(y2 – 2xy) – x(y3 – 5x2 ) (iii) 2x2 (x + 2) – 3x (x2 – 3) – 5x(x + 5) Q.2 Add the following polynomials. (i) x + y + xy, x – z + yx, and z + x + xz (ii) 2x2y 2– 3xy + 4, 5 + 7xy – 3x2y 2 , and 4x2y 2 + 10xy (iii) -3a2b 2 , (–5/2) a2b 2 , 4a2b 2 , and (2⁄3) a2b 2 Q.3 Subtract the following polynomials. (i) (7x + 2) from (-6x + 8) (ii) 3xy + 5yz – 7xz + 1 from -4xy + 2yz – 2xz + 5xyz + 1 (iii) 2x2y 2– 3xy + 4 from 4x2y 2 + 10xy Q.4 Simplify 7x2 (3x – 9) + 3 and find its values for x = 4 and x = 6 Q.5 Find the value of following using suitable identities : (b) (995)2 (c) (9.7)2 – (0.3)2 (d) 47 x 53 (e) (1005)2 (f) 9.8 X 10.2
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(i) (x+y+z)(x-y-z).
(x+y+z)(x−y−z) ( x + y + z ) ( x - y - z ).
Expand
(x+y+z)(x−y−z) ( x + y + z ) ( x - y - z ) by multiplying each term in term in the first expression by each term in the second expression.
Simplify terms
²-y²-yz-zy-z²
Subtract zy from -yz
x²-y²-2yz-z²
(ii) x²(x-3y²)-xy(y²-2xy)-x(y³-5x²)
x³-3x²y²-xy³+2x²y²-xy³+5x³
6x³-2xy³-x²y²
(iii) -7x²-2x(-7x²-2
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