Given, (5z 2)^2+40z [We know, (a b)^2=a^2 nbsp;2ab + b^2] ⇒ 25z^2 nbsp;20z + 4 + 40z ⇒ 25z^2 + 20z + 4 Factorizing, 25z^2+20z+4 ⇒(5z)^2 + 2×5z ×2+2^2 [W ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identities - Visualisation

5z-22 + 40z/5...

Question

$\frac{({(5 z - 2)}^{2} + 40 z)}{(5 z + 2)}$ =

2 z + 5

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(5 z - 2)^{2}

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5 z - 2

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5 z + 2

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Solution

The correct option is D $5 z + 2$
$G i v e n, (5 z - 2)^{2} + 40 z$
$[We know, (a - b)^{2} = a^{2} - 2 a b + b^{2}]$
$\Rightarrow 25 z^{2} - 20 z + 4 + 40 z$
$\Rightarrow 25 z^{2} + 20 z + 4$

$F a c t o r i z i n g, 25 z^{2} + 20 z + 4$
$\Rightarrow (5 z)^{2} + 2 \times 5 z \times 2 + 2^{2}$
$[We know, (a + b)^{2} = a^{2} + 2 a b + b^{2}]$
$\Rightarrow 25 z^{2} + 20 z + 4 = (5 z + 2)^{2}$
$∴ (5 z - 2)^{2} + 40 z = (5 z + 2)^{2}$

$So, \frac{({(5 z - 2)}^{2} + 40 z)}{(5 z + 2)} = \frac{(5 z + 2)^{2}}{(5 z + 2)}$
$= 5 z + 2$

Suggest Corrections

((5z−2)2+40z)(5z+2) =

The correct option is D 5z+2Given,(5z−2)2+40z [We know, (a−b)2=a2−2ab+b2] ⇒25z2−20z+4+40z ⇒25z2+20z+4 Factorizing, 25z2+20z+4 ⇒(5z)2+2×5z ×2+22 [We know, (a+b)2=a2+2ab+b2] ⇒25z2+20z+4=(5z+2)2 ∴(5z−2)2+40z=(5z+2)2 So, ((5z−2)2+40z)(5z+2)=(5z+2)2(5z+2) =5z+2

$\frac{({(5 z - 2)}^{2} + 40 z)}{(5 z + 2)}$ =