Answer
Answer :
(a)= ${a^2} - {b^2}$
(b)= $4{x^2} - 9{y^2}$
(c)= $16{x^2} - 49$
(d)= General Statement: ${x^2} -{y^2}$
Work Step by Step
Steps:
[A]
=(a+b)(a-b)
=a(a) - a(b) + a(b) -b(b)
=${a^2} -ab +ab - {b^2}$
= ${a^2} - {b^2}$
[B]
=(2x + 3y)(2x - 3y)
=2x(2x) - 2x(3y) + 2x(3y) - 3y(3y)
=$4{x^2} - 6xy +6xy - 9{y^2}$
= $4{x^2} - 9{y^2}$
[C]
=(4x+7)(4x-7)
=4x(4x) - 4x(7) + 4x(7) - 7(7)
=$16{x^2} - 28x + 28x - 49$
= $16{x^2} - 49$
[D]
General Statement:
(x+y)(x-y) = ${x^2} - {y^2}$
Proof:
(x+y)(x-y)
=${x^2} - x(y) + x(y)- {y^2}$
=${x^2} - {y^2}.$
