Short multiplication formulas [Polynomial identities]
Square of sum and difference, difference of squares, cube of sum and difference, sum and difference of cubes formulas.
Solved examples
Simplify the expression $(2x-5)^2$
$$(2x-5)^2=(2x)^2-2\cdot 2x\cdot 5 + 5^2=4x^2-20x+25$$Simplify the expression $(5x-4)(5x+4)$
$$(5x-4)(5x+4)=(5x)^2-4^2=25x^2-16$$Simplify the expression $(3x-2)^3$
$$(3x-2)^3=(3x)^3-3\cdot (3x)^2\cdot 2 + 3 \cdot 3x \cdot 2^2 - 2^3=27x^3-54x^2+36x-8$$Simplify the expression $(5x+1)^2-(5x+1)(5x-1)$
$$(5x+1)^2-(5x+1)(5x-1)=25x^2+10x+1-25x^2+1=10x+2$$Simplify the expression $(2+x)^3-(2+x)(4-2x+x^2)$
$$(2+x)^3-(2+x)(4-2x+x^2)=8+12x+6x^2+x^3-8-x^3=12x+6x^2$$Wanna check your skills?
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2020-11-28
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