Question

23- factorise :x² +8x+16​

Answer 1

Answer :

• x² + 8x + 16 = (x + 4)²

Given :

• x² + 8x+ 16

Solution :

Method (1)

》x² + 8x + 16

》x² + 4x + 4x + 16

》x(x + 4) + 4(x + 4)

》(x + 4)²

》(x + 4) (x + 4)

Method : (2)

》x² + 8x + 16

》x² + 2 × x × 4 + (4)²

》(x + 4)²

》(x + 4) (x + 4)

Hence , x² + 8x + 16 = (x + 4)²

Answer 2

• $\bf{\bold{x}^{2}}\:\bf{\bold{+\:8x\:+\:16}}$

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$\:\:\:\:\::\:\Longrightarrow\sf{x}^{2}\:\sf{+\:8x\:+\:16\:=\:0}$

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$\:\:\:\:\::\:\Longrightarrow\sf{x}^{2}\:\sf{(4\:+\:4)\:x\:+\:16\:=\:0}$

${ }$

$\:\:\:\:\::\:\Longrightarrow\sf{x}^{2}\:\sf{+\:4x\:+\:4x\:+\:16\:=\:0}$

${ }$

$\:\:\:\:\::\:\Longrightarrow\sf{x\:(x\:+\:4)\:+\:4\:(x\:+\:4)\:=\:0}$

${ }$

$\:\:\:\:\::\:\Longrightarrow\sf{x\:+\:4\:=\:0\:;\:x\:+\:4\:=\:0}$

${ }$

$\:\:\:\:\::\:\Longrightarrow\sf{\underline{\boxed{\bold{x\:=\:-4\:;\:x\:=\:-4}}}}\:★$