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Write these as a product

a) (2b–5)^2–36
b) 9–(7+3a)^2
c) (4–11m)^2–1

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1 Answer

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Answer

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 )

Step-by-step explanation

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 )

User Svyatoslav Danyliv
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