Question -
Answer -
i) (x2– 5) (x+ 5) + 25
= x3 +5x2 –5x – 25 + 25
= x3 +5x2 –5x
ii) (a2+ 5) (b3+ 3) + 5
= a2b3 + 3a2 +5b3 +15 + 5
= a2b3 + 5b3 +3a2 +20
iii) (t + s2)(t2 – s)
= t (t2 – s) + s2(t2 –s)
= t3 – st + s2t2 – s3
= t3 – s3 – st + s2t2
iv) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
= (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
=(ac – ad + bc – bd) + (ac + ad – bc – bd) + (2ac + 2bd)
= ac – ad + bc – bd + ac + ad – bc – bd + 2ac + 2bd
= 4ac
v) (x + y)(2x + y) + (x + 2y)(x – y)
= 2x2 +xy + 2xy + y2 + x2 – xy + 2xy – 2y2
= 3x2 +4xy – y2
vi) (x + y)(x2– xy + y2)
= x3 – x2y + xy2 + x2y – xy2 + y3
= x3 + y3
vii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
= 2.25x2 +6xy + 4.5x – 6xy – 16y2 –12y – 4.5x + 12y = 2.25x2 –16y2
viii) (a + b + c)(a + b – c)
= a2 +ab – ac + ab + b2 –bc + ac + bc – c2
= a2 + b2 – c2 +2ab