Extended Distributive Property: Is the equality correct?

Is the equation correct?

$a^2+9a-20=(a+4)(a-5)$

We solve the right side of the equation using the extended distributive property:$(a+b)\times(c+d)=ac+ad+bc+bd$

$(a+4)(a-5)=a^2-5a+4a-20$

$a^2-a-20$

That is, answer D is the correct one.

No, $-a$ instead of $+9a$

Is equality correct?

$(14+a)(a-2)=-2a^2+12a-28$

No, due to the coefficient of $a^2$

Is equality correct?

$(a+b)(c+d)=ab+cd+ac+bd$

No, it must be $ac+ad+bc+bd$

Is equality correct?

$(-2a+3b)(4c+5a)\stackrel{?}{=}8ac+10a^2-12bc-15ab$

No, the expression is exactly the same as$-(8ac+10a^2-12bc-15ab)$

Is equality correct?

$(b-3)(b+7)=b^2+4b-21$

Si

Is equality correct?

$(-4-x)(7+x)=-28-11x-x^2$

Si

Is equality correct?

$(4x+3)(8x+5)=32x^2+44x+15$

Si

Is equality correct?

$(2x-3)(-4+y)=-8x+2xy-3y+12$

Si

Is equality correct?

$(x+8)(2x-3)=2x^2+13x-24$

Si

Is equality correct?

$(3y+x)(4+2x)=2x^2+6xy+4x+12y$

Si

Are the expressions on both sides equivalent?

$5x^2+7x+7\stackrel{?}{=}(2x+3)(3x+4)$

No, because all the coefficients of the corresponding terms in the expressions on both sides of the equation are different.

Is equality correct?

$(y+9)(2y-2)=2y^2-20y+18$

No, it must be $(y-9)$ instead of $(y+9)$

Is equality correct?

$(a+4)(x+b+c)=ax+ab+ac+4$

No, it would be true if the expression were $(x+b+c)a+4$

Is equality correct?

$(x+8)(x-4)=(x-8)(x+4)$

No, the coefficients of$x$ In contrasting expressions