Question

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Answer 1

Answer:

Step-by-step explanation:

(i ) (xy + yx)² ⇒ (a+b)² = a² +2ab +b²

   = (xy)²+ 2(xy)(yx) + (yx)² = x²y² + 2x²y² + x²y² = 4x²y²

(ii) (x²y - xy²) ⇒ (a-b)² = a² -2ab +b²

  = (x²y)² -2(x²y)(xy²)² + (xy²) = $x^{4}$y² -2x³y³ + x²$y^{4}$

Answer 2

Answer:

(i)(xy+yz)²

Using the identity:-(a+b)²=a²+b²+2ab

a=xy, b=yz

=(xy)²+(yz)²+2(xy)(yz)

=x²y²+y²z²+2xy²z

(ii)(x²y-xy²)²

Using the identity:-(a-b)²=a²+b²-2ab

a=x²y, b=xy²

=(x²y)²+(xy²)²-2(x²y)(xy²)

=x^4y²+xy^4-2x³y³

$(iii) {( \frac{4}{5}a + \frac{5}{4} b)}^{2}$

$Using \: the \: identity:- \\ (a+b)²=a²+b²+2ab$

$a = \frac{4a}{5} , \: b = \frac{5b}{4}$

$= {( \frac{4a}{5}) }^{2} + {( \frac{5b}{4} )}^{2} + 2( \frac{4a}{5} )( \frac{5b}{4})$

$= \frac{16 {a}^{2} }{25} + \frac{25 {b}^{2} }{16} + \frac{20ab}{5}$

$= \frac{256 {a}^{2} + 625 {b}^{2} + 1600ab}{400}$