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Solve the question Algebraic Expressions

(i) (2.5p − 1.5q)2 − (1.5p − 2.5q)2

(ii) (ab + bc)2 − 2ab2

(iii) (m2 − n2m)2 + 2m3n2

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(i) (2.5p − 1.5q)2 − (1.5p − 2.5q)2

= (2.5p)2 − 2(2.5p) (1.5q) + (1.5q)2 − [(1.5p)2 − 2(1.5p)(2.5q) + (2.5q)2] [(a − b)2 = a2 − 2ab + b2 ]

= 6.25p2 − 7.5pq + 2.25q2 − [2.25p2 − 7.5pq + 6.25q2]

= 6.25p2 − 7.5pq + 2.25q2 − 2.25p2 + 7.5pq − 6.25q2]

= 4p2 − 4q2

(ii) (ab + bc)2 − 2ab2c

= (ab)2 + 2(ab)(bc) + (bc)2 − 2ab2c [(a + b)2 = a2 + 2ab + b2 ]

= a2b2 + 2ab2c + b2c2 − 2ab2c

= a2b2 + b2c2

(iii) (m2 − n2m)2 + 2m3n2

= (m2)2 − 2(m2) (n2m) + (n2m)2 + 2m3n2  [(a − b)2 = a2 − 2ab + b2 ]

= m4 − 2m3n2 + n4m2 + 2m3n2

= m4 + n4m2

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