Question

Solve using identities
a. (3x+2y)(3x-2y)
b. (4x+5)(4x+5)
c. (2x-3y)²
d. 68²-12²
e. 102²

Answer 1

hope this will help you

Answer 2

FULL ANSWER WITH STEPS

ANSWER a
$(3x+2y)(3x-2y)$
$=(3x)^{2}-(2y)^{2}$   [Using the identity $(a+b)(a-b)=a^{2}-b^{2}$]
$=9x^{2}-4y^{2}$

ANSWER b
$(4x+5)(4x+5)$
$=(4x+5)^{2}$              [∵ $a*a=a^{2}$]
$=(4x)^{2}+2(4x)(5)+5^{2}$  [Using the identity $(a+b)^{2}=a^{2}+2ab+b^{2}$]
$=16x^{2}+40x+25$

ANSWER c
$(2x-3y)^{2}$
$(2x)^{2}-2(2x)(3y)+(3y)^{2}$    [Using the identity $(a-b)^{2}=a^{2}-2ab+b^{2}$]
$=4x^{2}-12xy+9y^{2}$

ANSWER d
$68^{2}-12^{2}$
$=(68+12)(68-12)$    [Using the identity $(a+b)(a-b)=a^{2}-b^{2}$
$=80*56$
$=4480$

ANSWER e
$102^{2}$
$=(100+2)^{2}$
$=100^{2}+2(100)(2)+2^{2}$    [Using the identity $(a+b)^{2}=a^{2}+2ab+b^{2}$]
$=10000+400+4$
$=10404$

Hope these may help you. 

If you have any doubt, then you can ask me in the comments.