Find the product of the following binomials:(i) (2x + y) (2x + y)(ii

1.	Find the product of the following binomials:(i) (2x + y) (2x + y)(ii) (a + 2b) (a – 2b)(iii) (a2 + bc) (a2 – bc)
Answer» (i) (2x + y) (2x + y) = 2x(2x + y) + y(2x + y) = 4x² + 2xy + 2xy + y² = 4x² + 4xy + y² (ii) (a + 2b) (a – 2b) = a(a – 2b) + 2b (a – 2b) = a² – 2ab + 2ab – 4b² = a² – 4b² (iii) (a²+ bc) (a² – bc) = a² (a² – bc) + bc (a² – bc) = a⁴ – a²bc + bca² – b²c² = a⁴ – b²c²

Find the product of the following binomials:(i) (2x + y) (2x + y)(ii) (a + 2b) (a – 2b)(iii) (a2 + bc) (a2 – bc)

Answer»

(i) (2x + y) (2x + y)

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

= 4x² + 2xy + 2xy + y²

= 4x² + 4xy + y²

(ii) (a + 2b) (a – 2b)

= a(a – 2b) + 2b (a – 2b)

= a² – 2ab + 2ab – 4b²

= a² – 4b²

(iii) (a²+ bc) (a² – bc)

= a² (a² – bc) + bc (a² – bc)

= a⁴ – a²bc + bca² – b²c²

= a⁴ – b²c²

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