Question

PLEASE HELP!!!

Replace ∗ with a monomial so that the result is an identity:
A.
(2a+∗)(2a−∗)=4a^2–b^2

Answer:
(2a + __)(2a − __) = 4a^2 − b^2

B.
(5x+∗)(5x−∗)=25x^2–0.16y^4
Answer:
(5x + __)(5x −__) = 25x^2 − 0.16y^4

Answer 1

$\underline { \blue{By\: Algebraic \: Identity: }}$

$\boxed { \pink { m^{2} - n^{2} = ( m + n )( m - n ) }}$

$A. ( 2a + \_ )( 2a - \_ ) = 4a^{2} - b^{2}$

$RHS = 4a^{2} - b^{2} \\= (2a)^{2} - b^{2} \\= ( 2a + \pink {b} )( 2a - \pink {b} )$

$B. ( 5x + \_ )( 5x -\_ ) = 25x^{2} - 0.16y^{4}$

$RHS = 25x^{2} - 0.16y^{4}\\= (5x)^{2} - (0.4y^{2})^{2} \\= ( 5x +\pink {0.4y^{2} })( 5x - \pink { 0.4y^{2}} )$

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