Question

Expand by using suitable identities:
(i) (x²+y²)(x²-y²)
(ii) (0.9p+0.5q)²​

Answer 1

Answer:

(i)(x² + y²)(x - y)(x + y)

(ii)0.81p² + 0.9pq + 0.25q²

Step-by-step explanation:

(i) (x²+y²)(x²-y²)                             (a²-b²)= (a)²-(b)²

=> (x² + y²){(x)²-(y)²}                            

=>(x² + y²)(x - y)(x + y)

(ii) (0.9p+0.5q)²​

=> (0.9p)² + 2(0.9p × 0.5q) + (0.5q)²            (a+b)²=a²+2ab+b²

=> 0.81p² + 0.9pq + 0.25q²

HOPE THE ANSWER HELPED!!

Answer 2

• (i)(x² + y²)(x - y)(x + y)
• (ii)$\displaystyle{\sf{ (0.9p-0.5q)^{2}}}$

$\Large{\underbrace{\sf{\red{Required\:Solution:}}}}$

(i) (x²+y²)(x²-y²)                            

Using Identity - (a²-b²)= (a)²-(b)²

=> (x² + y²){(x)²-(y)²}                            

=>(x² + y²)(x - y)(x + y)

and

• (ii)$\displaystyle{\sf{ (0.9p-0.5q)^{2}}}$

Using Identity - (α-b)² = α²-2αb+b²

$\longrightarrow{\sf{ (0.9p)^{2} - 2\times (0.9p)\times (0.5q) + (0.5q)^{2}}}$

$\longrightarrow{\sf{ 0.81p^{2} - (1.8p)\times (0.5q)+0.25q^{2}}}$

$\large\implies{\boxed{\sf{\red{ 0.81p^{2} - 0.9pq+ 0.25q^{2}}}}}$

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$\Large{\underbrace{\sf{\orange{Explore\:More!}}}}$

• Algebrαic identity - An αlgebrαic identity is αn equαlity thαt holds for αny vαlues of its vαriαbles.

There αre some αlgebrαic identities —

• (a+b)² = a² + 2ab + b²
• (a-b)² = a² - 2ab + b²
• a²-b² = (a-b)(a+b)
• a²+b² = (a+b)² - 2ab
• (x+a)(x+b) = x² + (a+b)x + ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ - b³ - 3ab(a-b)
• a³+b³ = (a+b)³-3ab(a+b)

⠀⠀⠀⠀⠀⠀= (a+b) (a²- ab + b²)

• a³-b³ = (a-b)³+3ab(a-b)
• ⠀⠀⠀⠀⠀⠀⠀= (a-b) (a² + ab + b²)

• (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a-b-c)² = a² + b² + c² - 2ab + 2bc - 2ca
• (a-b+c)² = a² + b² + c² - 2ab - 2bc + 2ca

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