Question

expand each of the following using suitable identities [ - x + 2y – 5z]2

Answer 1

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Here we use the identity,

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

(-x + 2y - 5z)²

= (-x)² + (2y)² + (-5z)² + 2(-x)(2y) + 2(2y)(-5z) + 2(-x)(-5z)

= x² + 4y² + 25z² - 4xy - 20yz + 10xz

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Answer 2

$\huge\sf\pink{Answer}$

☞ x²+4y²+25z²-4xy-20yz+10xz

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ 2(-x+2y-5z)

$\rule{110}1$

$\huge\sf\gray{To \:Do}$

◈ Expand using identity

$\rule{110}1$

$\huge\sf\purple{Steps}$

➝ $\sf( -x+2y-5Z) {}^{2}\qquad \bigg\lgroup (a+b+x)^2 = a^2+b^2+c^2+2ab+2bc+2ca\bigg\rgroup$

➝ $\sf (-x)^2 + (2y)^2+(-5z)^2 + 2(-x)(2y) + 2(2y)(-5z) + 2(-x)(-5z)$

➝ $\sf x^2 + 4y^2+25z^2-4xy-20yz+10xz$

$\rule{170}3$