Answer
a) $14x+7$
b) $x^{2}-2x-15$
c) $6x^{2}+x-2$
d) $a^{2}-4b^{2}$
e) $y^{2}-6y+9$
f) $4x^{2}+20x+25$
Work Step by Step
a) $14x+7$
$4(x+3)+5(2x-1)=4x+12+10x-5$ (Use the distributive property)
$4x+12+10x-5=14x+7$ (Combine like terms)
b) $x^{2}-2x-15$
$(x+3)(x-5)=x(x-5)+3(x-5)$ (Distribute the first parenthesis)
$x(x-5)+3(x-5)=x^{2}-5x+3x-15$ (Distribute the x and 3)
$x^{2}-5x+3x-15=x^{2}-2x-15$ (Combine like terms)
c) $6x^{2}+x-2$
$(2x-1)(3x+2)=6x^{2}-3x+4x-2$ (Use FOIL, which is basically doing the same thing as in part b, but skipping a step)
$6x^{2}-3x+4x-2=6x^{2}+x-2$ (Combine like terms)
d) $a^{2}-4b^{2}$
$(a-2b)(a+2b)=a^{2}-(2b)^{2}$ (Using the difference of two squares formula)
$a^{2}-(2b)^{2}=a^{2}-4b^{2}$ (Distributing the exponent)
e) $y^{2}-6y+9$
$(y-3)^{2}=(y-3)(y-3)$ (Rewriting the expression)
$(y-3)(y-3)=y^{2}-3y-3y+9$ (FOILing the expression)
$y^{2}-3y-3y+9=y^{2}-6y+9$ (Combine like terms)
f) $4x^{2}+20x+25$
$(2x+5)^{2}=(2x+5)(2x+5)$ (Rewriting the expression)
$(2x+5)(2x+5)=4x^{2}+10x+10x+25$ (FOILing the expression)
$4x^{2}+10x+10x+25=4x^{2}+20x+25$ (Combine like terms)
