Question

Evaluate the product $(5a-3b)(4a+7b)$ using distributive property.

• A. $20a^2+23ab-21b^2$
• B. $20a^2-23ab+21b^2$
• C. $20a^2+23ab+21b^2$
• D. $20a^2-23ab-21b^2$

Answer 1

The correct option is A $20a^2+23ab-21b^2$

$\underset{–}{\text{Distributive Property of Multiplication}:}$
It is defined as the algebraic property used to multiply two or more numbers or algebraic expressions within the parenthesis. We can say that the distributive property helps in simplifying the problems by breaking the expressions into addition or subtraction. It multiplies the number or algebraic expression outside parentheses which is equal to the addition or sum of product.

For example, $7(5+2)=7\times 5+7\times 2$

$7\left(7\right)=35+14$

$49=49$

We need to find the value of the product $(5a-3b)(4a+7b)$ using distributive property.

The product $(5a-3b)(4a+7b)$ can be evaluated as:

$(5a-3b)(4a+7b)$
$=\underset{–}{5a(4a+7b)}-\underset{–}{3b(4a+7b)}$
$=\underset{–}{(5a\times 4a)}+\underset{–}{(5a\times 7b)}-\underset{–}{(3b\times 4a)}-\underset{–}{(3b\times 7b)}$
$=\left(20a^{1+1}\right)+\left(35ab\right)-\left(12ab\right)-\left(21b^{1+1}\right)\because (a^m\times a^n=a^{m+n})$
$=20a^2+35ab-12ab-21b^2$
$=20a^2+\underset{–}{35ab-12ab}-21b^2$
$=20a^2+23ab-21b^2$

The value of the product $(5a-3b)(4a+7b)$ evaluated using distributive property is $20a^2+23ab-21b^2$.
Therefore, option (a.) is the correct answer.