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malfutka [58]
3 years ago
6

Write these as a product

Mathematics
1 answer:
Oxana [17]3 years ago
4 0

<u>Ans</u><u>wer</u>

a)

{(2b - 5)}^{2}  - 36 =( 2b - 11)(2b  +  1)

b)

9 -  {(7 + 3a)}^{2}  =  (3a - 4)(3a + 11)

c)

( {4 - 11m)}^{2}  - 1 =( 3 - 11m )( 5 - 11m )

<u>Explanation</u>

a) The given expresion is

{(2b - 5)}^{2}  - 36

We rewrite as difference of two squares

{(2b - 5)}^{2}  - 36 = {(2b - 5)}^{2}  -  {6}^{2}

Recall that:

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

This implies that:

{(2b - 5)}^{2}  - 36 =( {(2b - 5)} -6)(2b - 5 )+ 6)

Or

{(2b - 5)}^{2}  - 36 =( 2b - 5-6)(2b - 5 + 6)

This simplifies to give:

{(2b - 5)}^{2}  - 36 =( 2b - 11)(2b  +  1)

b) The second expression is

9 -  {(7 + 3a)}^{2}

We rewrite as perfect squares yo get:

9 -  {(7 + 3a)}^{2}  =  {3}^{2} -  {(7 + 3a)}^{2}

This gives:

9 -  {(7 + 3a)}^{2}  =  ({3} -  {(7 + 3a)})({3}  +  {(7 + 3a)})

This implies that

9 -  {(7 + 3a)}^{2}  =  ({3} -  7 + 3a)({3}  + 7 + 3a)

We simplify to get:

9 -  {(7 + 3a)}^{2}  =  (3a - 4)(3a + 11)

c) The third expression is:

( {4 - 11m)}^{2}  - 1

We obtain the difference of two squares as:

( {4 - 11m)}^{2}  - 1 =( ( {4 - 11m)}  - 1 )( ( {4 - 11m)}  + 1 )

We simplify within the parenthesis to get:

( {4 - 11m)}^{2}  - 1 =( 4 - 11m  - 1 )( 4 - 11m+ 1 )

We simplify further to get;

( {4 - 11m)}^{2}  - 1 =( 3 - 11m )( 5 - 11m )

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