Question

Match the expression on the left with the correct simplified expression on the right.

(x+4)²
(x+4)(x-4).
x²
x²16
x² + 16
x² + 8x + 16
x² + 16x + 16

Answer 1

1) (x + 4)²

By Using Identity:-

`\quad \hookrightarrow \: { \underline{ \overline{ \boxed{ \pmb{ \sf{ {(a + b)}^(2) = \: {a}^(2) + {b}^(2) + 2ab \: }}}}}} \: \red \bigstar \\`

`\sf \longrightarrow \: {(x + 4)}^(2)`

`\sf \longrightarrow \: {x}^(2) + {4}^(2) + 2 * 4 * x`

`\sf \longrightarrow \: {x}^(2) + {4}^(2) + 8 * x`

`\sf \longrightarrow \: {x}^(2) + {4}^(2) + 8 x`

`\sf \longrightarrow \: {x}^(2) + 16 + 8 x`

`\sf \longrightarrow \: {x}^(2) + 8 x + 16`

Therefore ,

• (x+4)² = x² + 8x + 16

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2) ( x+4 ) ( x-4 )

`\sf \longrightarrow \: ( x+4 ) ( x-4 )`

`\sf \longrightarrow \: x ( x - 4 ) + 4( x-4 )`

`\sf \longrightarrow \: {x}^(2) - 4x + 4x - 16`

`\sf \longrightarrow \: {x}^(2) - 0 - 16`

`\sf \longrightarrow \: {x}^(2) -16`

Therefore,

• ( x+4 ) ( x-4 ) = x² - 16

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