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Volgvan
2 years ago
11

Write the expression as a product: 1–(2x–1)^2

Mathematics
1 answer:
postnew [5]2 years ago
3 0

Answer:

1- ( { 2 x - 1)}^{2} =  4x (1  - x )

Step-by-step explanation:

We want to to rewrite

1 - ( { 2 x - 1)}^{2}

Use difference of two squares to get:

{a}^{2}  -  {b}^{2}  = (a + b)(a - b)

This implies that:

{1}^{2} - ( { 2 x - 1)}^{2}  = (1 +( 2x - 1))(1  - (2x  - 1))

{1}^{2} - ( { 2 x - 1)}^{2}  = (1 + 2x - 1)(1  - 2x   + 1)

This finally simplifies to:

{1}^{2} - ( { 2 x - 1)}^{2}  =  2x (2  - 2x )

Therefore the required product is

2x (2  - 2x ) = 4x(1 - x)

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2 years ago
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2 years ago
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