Evaluate the value of the product 3x-4y- 8x-5y and find the numerical coefficient of xy-

Step 1: Evaluating the product using FOIL rule: (3x 4y)× (8x+5y) = 3x× (8x+5y) 4y× (8x+5y) = 3x× (8x+5y) 4y× (8x+5y) = (3x× 8x)+ (3x× 5y) (4y× 8x) (4y× 5 ...

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Byju's Answer

Standard VII

Mathematics

Types of Coefficients

Evaluate the ...

Question

Evaluate the value of the product $(3 x - 4 y) \times (8 x + 5 y)$ and find the numerical coefficient of $x y$ .

Product

= 24 x^{2} - 17 x y - 20 y^{2}

Coefficient of

x y = 24

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Product

= 24 x^{2} + 17 x y - 20 y^{2}

Coefficient of

x y = - 17

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Product

= 24 x^{2} - 24 x y - 20 y^{2}

Coefficient of

x y = - 24

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Product

= 24 x^{2} - 20 x y - 20 y^{2}

Coefficient of

x y = - 20

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Solution

The correct option is B Product $= 24 x^{2} + 17 x y - 20 y^{2}$
Coefficient of $x y = - 17$
$S t e p 1 : - ------ -$

Evaluating the product using FOIL rule:
$(3 x - 4 y) \times (8 x + 5 y)$
$= 3 x \times (8 x + 5 y) - 4 y \times (8 x + 5 y)$
$= 3 x \times (8 x + 5 y) - -------------- - - 4 y \times (8 x + 5 y) - -------------- -$
$= (3 x \times 8 x) + (3 x \times 5 y) - (4 y \times 8 x)$
$- (4 y \times 5 y)$
$= 24 x^{2} + 15 x y - 32 x y - 20 y^{2}$ ( Since $a^{m} \times a^{n} = a^{m + n}$ )
$= 24 x^{2} - 17 x y - 20 y^{2}$

The value of the product $(3 x - 4 y) \times (8 x + 5 y)$ is $24 x^{2} - 17 x y - 20 y^{2}$ .

$S t e p 2 : - ------ -$

The value of the product $(3 x - 4 y) \times (8 x + 5 y)$ is $24 x^{2} - 17 x y - 20 y^{2}$ .
Coefficient of $x^{2}$ in the product $= 24$
Coefficient of $x y$ in the product $= - 17$
Coefficient of $y^{2}$ in the product $= - 20$

Therefore, option (b.) is the correct answer.

Suggest Corrections

Evaluate the value of the product (3x−4y)×(8x+5y) and find the numerical coefficient of xy.

Evaluate the value of the product $(3 x - 4 y) \times (8 x + 5 y)$ and find the numerical coefficient of $x y$ .