Question

16x² - 40xy + 25y²
Factorize by using appropriate identities.

Answer 1

BONJOUR,
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$16 {x}^{2} - 40xy + 25 {y}^{2} \\ \ \: we \: can \: write \: this \: like \: \\ (4x) {}^{2} - 2 \times 4x \times 5y + (5y) {}^{2} \\ (4x - 5y)(4x - 5y) \\ (4x - 5y) {}^{2} \\ hope \: it \: helps \\ here \: we \: use \: the \: identity \: (x - y) {}^{2} = x {}^{2} - 2xy + y {}^{2}$

Answer 2

Hi ,

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We know the algebraic identity :

a² - 2ab + b² = ( a - b )²
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Here ,

It is given that ,

16x² - 40xy + 25y²

= ( 4x )² - 2 ×( 4x ) ×( 5y ) + ( 5y )²

= ( 4x - 5y )²

= ( 4x - 5y )( 4x - 5y )

I hope this helps you.

: )