I can use the distributive law to multiply multiple expressions by their respective terms and then simplify by collecting like terms
I can use the distributive law to multiply multiple expressions by their respective terms and then simplify by collecting like terms
Simplify - To simplify an expression is to write it in a more efficient and compact form without affecting the value of the original expression.
Like terms - Like terms are terms that have the same set of variables and corresponding exponents.
Pupils may think 5(y+1)-2(y+3) = 5y+5-2y+6
Correct use of the distributive law with either algebra tiles or an area model will demonstrate why this is wrong.
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$$3x + 7 + 4x + 6$$ -Â $$7x +13$$
$$7x + 3 + 6x + 4$$ -Â $$13x + 7$$
$$7x + 13 + 3x -3$$ -Â $$10x+10$$
$$6x -7 -13x -3 $$ -Â $$-7x-10$$
$$3x + 13 + 4x -3$$ -Â $$7x+10$$
$$7(y+3)$$ -Â $$7y+21$$
$$-7(y-3)$$ -Â $$21-7y$$
$$-7(y+3)$$ -Â $$-7y-21$$
$$7(y-3)$$ -Â $$7y-21$$
$$5(x+4)+3(x+8)$$ -Â $$8x+44$$
$$5(x+4)+8(x+3)$$ -Â $$13x+44$$
$$4(x+5)+3(x+8)$$ -Â $$7x+44$$
$$4(x+5)+8(x-3)$$ -Â $$12x-4$$
$$4(x-5)+8(x+3)$$ -Â $$12x+4$$
$$x(x+y-7)-3x(x-2y)$$ -Â $$-2x^2-7x+7xy$$
$$x(x+y-7)+3x(x-2y)$$ -Â $$4x^2-7x-5xy$$
$$-x(x+y-7)+3x(x-2y)$$ -Â $$2x^2+7x-7xy$$
$$-x(x+y-7)-3x(x-2y)$$ -Â $$-4x^2+7x+5xy$$
