Question

multiply the given pair of binomial: ​

Answer 1

Answer:

1)b^4-a^4

2)36x^2-49

3)a^2-2ac+c^2

4)4x^2+16x+12y+9y^2

5)49a^2-126ab+81b^2

Answer 2

Step-by-step explanation:

We Have :-

$(1) \: \: \: \: (a^{2} + b^{2} )( - a^{2} + b^{2} ) \\ \\ \\ (2) \: \: \: \: (6x - 7)(6x + 7) \\ \\ \\ (3) \: \: \: \: ( - a + c)( - a + c) \\ \\ \\ (4) \: \: \: \: ( \dfrac{x}{2} + \dfrac{3y}{4} )( \dfrac{x}{2} + \dfrac{3y}{4} ) \\ \\ \\ (5) \: \: \: \: (7a - 9b)(7a - 9b)$

To Find :-

$multiply \: them$

Identity Used :-

$(a + b)(a - b) = a^{2} - b^{2} \\ \\ \\ (a + b)^{2} = a^{2} + b^{2} + 2ab \\ \\ \\ (a - b)^{2} = a^{2} + b^{2} - 2ab$

Solution :-

$(1) \: \: \: \: (a^{2} + b^{2} )( - a^{2} + b^{2} ) \\ \\ \\ a^{2}( - a^{2} + b^{2} ) + b^{2}( - a^{2} + b^{2} ) \\ \\ \\ - a^{4} + a^{2} b^{2} -a^{2} b^{2} + b^{4} \\ \\ \\ b^{4} - a ^{4} \\ \\ \\ \\ (2) \: \: \: \: (6x - 7)(6x + 7) \\ \\ \\ using \: idetity \\ \\ \\ (6x)^{2} - (7) ^{2} \\ \\ \\ 36x^{2} - 49 \\ \\ \\ \\ (3) \: \: \: \: ( - a + c)( - a + c) \\ \\ \\ using \: identity \\ \\ \\ ( - a + c)^{2} \\ \\ \\ a^{2} + c^{2} + 2( - a)c \\ \\ \\ a^{2} + c^{2} - 2 ac \\ \\ \\ \\ (4) \: \: \: \: ( \dfrac{x}{2} + \dfrac{3y}{4} )( \dfrac{x}{2} + \dfrac{3y}{4} ) \\ \\ \\ using \: identity \\ \\ \\( \dfrac{x}{2} + \dfrac{3y}{4} )^{2} \\ \\ \\ ( \dfrac{x}{2})^{2} + ( \dfrac{3y}{4})^{2} \\ \\ \\ \dfrac{x^{4} }{4} + \dfrac{9y ^{2} }{16} + 2 (\dfrac{x}{2} )( \dfrac{3y}{4}) \\ \\ \\ \dfrac{x^{2} }{4} + \dfrac{9y ^{2} }{16} + \dfrac{3xy}{4} \\ \\ \\ \dfrac{4x^{2} + 9y ^{2} + 12xy}{16} \\ \\ \\ \\ (5) \: \: \: \: (7a - 9b)(7a - 9b) \\ \\ \\ using \: identity \\ \\ \\ (7a - 9b)^{2} \\ \\ \\ (7a)^{2} + (9b)^{2} - 2(7a)(9b) \\ \\ \\ 49a^{2} + 81b^{2} - 126ab$