Expand the expression (4a-7b-9c-5d)^2

 Exercise

$\left(4a-7b-9c-5d\right)^2$

 

Expand the trinomial using the formula $\left(a+b+c\right)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc$

$\left(4a\right)^2+\left(-7b\right)^2+\left(-9c-5d\right)^2-56ab+8a\left(-9c-5d\right)-14b\left(-9c-5d\right)$

 

The power of a product is equal to the product of it's factors raised to the same power

$16a^2+\left(-7b\right)^2+\left(-9c-5d\right)^2-56ab+8a\left(-9c-5d\right)-14b\left(-9c-5d\right)$

 

Multiply the single term $8a$ by each term of the polynomial $\left(-9c-5d\right)$

$16a^2+\left(-7b\right)^2+\left(-9c-5d\right)^2-56ab-72ca-40da-14b\left(-9c-5d\right)$

 

Multiply the single term $-14b$ by each term of the polynomial $\left(-9c-5d\right)$

$16a^2+\left(-7b\right)^2+\left(-9c-5d\right)^2-56ab-72ca-40da+126cb+70db$

 

Expand $\left(-9c-5d\right)^2$

$16a^2+\left(-7b\right)^2+\left(-9c\right)^2+90cd+\left(-5d\right)^2-56ab-72ca-40da+126cb+70db$

$16a^2+\left(-7b\right)^2+\left(-9c\right)^2+90cd+\left(-5d\right)^2-56ab-72ca-40da+126cb+70db$

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