Question

class 8 maths ch 9 ex 9.4 que no 3​

Answer 1

Answer:

(i) (x2 – 5) (x + 5) + 25

= x2(x + 5) + 5(x + 5) + 25

= x3 + 5x2 – 5x – 25 + 25

= x3 + 5x2 – 5x + 0

= x3 + 5x2 – 5x

(ii) (a2 + 5)(b3 + 3) + 5

= a2(b3 + 3) + 5(b3 + 3) + 5

= a2b3 + 3a2 + 5b3 + 15 + 5

= a2b3 + 3a2 + 5b3 + 20

(iii) (t + s2) (t2 – s)

= t(t2 – s) + s2(t2 – s)

= t3 – st + s2t2 – s3

= t3 + s2t2 – st – s3

(iv) (a + b)(c – d) + (a – b) (c + d) + 2(ac + bd)

= a(c – d) + b(c – d) + a(c + d) – b(c + d) + 2ac + 2bd

= ac – ad + bc – bd + ac + ad – bc – bd + 2ac + 2bd

= ac + ac + 2ac + bc – bc – ad + ad – bd – bd + 2bd

= 4ac + 0 + 0 + 0

= 4ac

(v) (x + y) (2x + y) + (x + 2y) (x – y)

= x(2x + y) + y(2x + y) + x(x – y) + 2y(x – y)

= 2x2 + xy + 2xy + y2 + x2 – xy + 2xy – 2y2

= 2x2 + x2 + xy + 2xy – xy + 2xy + y2 – 2y2

= 3x2 + 4xy – y2

(vi) (x + y)(x2 – xy + y2)

= x(x2 – xy + y2) + y(x2 – xy + y2)

= x3 – x2y + x2y + xy2 – xy2 + y3

= x3 – 0 + 0 + y3

= x3 + y3

(vii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x.+ 12y

= 1.5x (1.5x + 4y + 3) – 4y(1.5x + 4y + 3) – 4.5x + 12y

= 2.25x2 + 6xy + 4.5x – 6xy – 16y2 – 12y – 4.5x + 12y

= 2.25x2 + 6xy – 6xy + 4.5x – 4.5x + 12y – 12y – 16y2

= 2.25x2 + 0 + 0 + 0 – 16y2

= 2.25x2 – 16y2

(viii) (a + b + c) (a + b – c)

= a(a + b – c) + b(a + b – c) + c(a + b – c)

= a2 + ab – ac + ab + b2 – bc + ac + bc – c2

= a2 + ab + ab – bc + bc – ac + ac + b2 – c2

= a2 + 2ab + b2 – c2 + 0 + 0

= a2 + 2ab + b2 – c2

Step-by-step explanation:

hope it will help u