We use distributive property to multiply or divide an algebraic expression by rational number or algebraic term. Rules of integers, rational numbers are also true for algebra. Also children should know basic exponential rules
a. a. a. a. a. a = a6 where a is base and 6 is exponent/index/power.
Distributive property
a(b + c) = ab + ac
3(4+5) = 3 x 4 + 3 x 5
- Multiply 3x2 -5x +4 by -2
-2(3x2-5x+4)= -2(3x2)-2(-5x)-2(4)
= -6x2+10x-8
2. Divide (6x2 -10x +4) by -2
=\frac{6x^2}{-2}\:-\frac{10x}{-2}\:+\frac{4}{-2}\:-3x^2+5x-2
3. Multiply 2m2 n and (-3m+4n2 – 4mn)
2m2n(-3m+4n2-4mn)= -6m3n + 8m2n3 - 8m3n2 Answer!
4. Divide
4a^2\:b^2\:\:-2abc\:+3abd\:by\:-\frac{1}{2}\:ab\frac{4a^2\:b^2\:\:-2abc\:+3abd\:\:}{-\frac{1}{2}\:ab}-\frac{4a^2b^2+3abd-2abc}{\frac{ab}{2}}2 will go to the numerator
-\frac{2\left(4a^2b^2+3abd-2abc\right)}{ab}=-2\left(4ab+3d-2c\right) = -2(4ab + 3d - 2c) Answer!
5. Divide
\frac{3}{4}x^2y^{2\:}-\frac{1}{6}xy^2\:+\frac{1}{2}x^2y\:by\:-\frac{12x}{y}\frac{\frac{3}{4}x^2y^2-\frac{1}{6}xy^2+\frac{1}{2}x^2y}{-\frac{12x}{y}}Divide each term,
\frac{\frac{3}{4}x^2y^2}{-\frac{12x}{y}}=-\frac{xy^3}{16};-\frac{\frac{1}{6}xy^2}{-\frac{12x}{y}}=\frac{y^3}{72}; \frac{\frac{1}{2}x^2y}{-\frac{12x}{y}}=-\frac{xy^2}{24}-\frac{xy^3}{16}+\frac{y^3}{72}-\frac{xy^2}{24}Simplify and take out y2 and common denominator 144
= -\frac{y^2\left(9xy+6x-2y\right)}{144}Answer!