Find the product of the following binomials:(i) (4x/5 – 3y/4) (4x/

1.	Find the product of the following binomials:(i) (4x/5 – 3y/4) (4x/5 + 3y/4)(ii) (2x + 3/y) (2x – 3/y)(iii) (2a3 + b3) (2a3 – b3)
Answer» (i) (4x/5 – 3y/4) (4x/5 + 3y/4) = 4x/5 (4x/5 + 3y/4) – 3y/4 (4x/5 + 3y/4) = 16/25x² + 12/20yx – 12/20xy – 9y²/16 = 16/25x² – 9/16y² (ii) (2x + 3/y) (2x – 3/y) = 2x (2x – 3/y) + 3/y (2x – 3/y) = 4x² – 6x/y + 6x/y – 9/y² = 4x² – 9/y² (iii) (2a³ + b³) (2a³ – b³) = 2a³ (2a³ – b³) + b³ (2a³ – b³) = 4a⁶ – 2a³b³ + 2a³b³ – b⁶ = 4a⁶ – b⁶

Find the product of the following binomials:(i) (4x/5 – 3y/4) (4x/5 + 3y/4)(ii) (2x + 3/y) (2x – 3/y)(iii) (2a3 + b3) (2a3 – b3)

Answer»

(i) (4x/5 – 3y/4) (4x/5 + 3y/4)

= 4x/5 (4x/5 + 3y/4) – 3y/4 (4x/5 + 3y/4)

= 16/25x² + 12/20yx – 12/20xy – 9y²/16

= 16/25x² – 9/16y²

(ii) (2x + 3/y) (2x – 3/y)

= 2x (2x – 3/y) + 3/y (2x – 3/y)

= 4x² – 6x/y + 6x/y – 9/y²

= 4x² – 9/y²

(iii) (2a³ + b³) (2a³ – b³)

= 2a³ (2a³ – b³) + b³ (2a³ – b³)

= 4a⁶ – 2a³b³ + 2a³b³ – b⁶

= 4a⁶ – b⁶

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