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Question

Factorise $${ \left( 4x+y \right)  }^{ 2 }+\left( 4x+y \right) \left( x+2y \right) -20{ \left( x+2y \right)  }^{ 2 }$$.


A
(9x+11y)(x+9y)
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B
(9x+11y)(x9y)
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C
(9x+11y)(7y)
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D
(9x11y)(x9y)
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Solution

The correct option is C $$-\left( 9x+11y \right) \left( 7y \right) $$
$${ \left( 4x+y \right)  }^{ 2 }+\left( 4x+y \right) \left( x+2y \right) -20{ \left( x+2y \right)  }^{ 2 }$$.
We know, $$(a+b)^2=a^2+2ab+b^2$$

$$\Rightarrow$$  $$16x^2+8xy+y^2+4x^2+8xy+xy+2y^2-20(x^2+4xy+4y^2)$$

$$\Rightarrow$$  $$20x^2+17xy+3y^2-20x^2-80xy-80y^2$$

$$\Rightarrow$$  $$-63xy-77y^2$$

$$\Rightarrow$$  $$(7y)(-9x-11y)$$

$$\Rightarrow$$  $$-(9x+11y)(7y)$$

Mathematics

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