Multiplying and simplifying with multiple expressions | Maths

Starter quiz

Without changing its value, we could write the expression $5x+7+3x+8$ more efficiently by ______ it.

'simplifying' ✓
Expand $8(x+3)$

$8+x+3$

$8x+24$ ✓

$8x+3$

$x+24$
Match the expressions to the simplified expressions.

$3x + 7 + 4x + 6$

⇔

$7x +13$ ✓

$7x + 3 + 6x + 4$

⇔

$13x + 7$ ✓

$7x + 13 + 3x -3$

⇔

$10x+10$ ✓

$6x -7 -13x -3$

⇔

$-7x-10$ ✓

$3x + 13 + 4x -3$

⇔

$7x+10$ ✓
Match the expressions.

$7(y+3)$

⇔

$7y+21$ ✓

$-7(y-3)$

⇔

$21-7y$ ✓

$-7(y+3)$

⇔

$-7y-21$ ✓

$7(y-3)$

⇔

$7y-21$ ✓
Simplify $10x+3-7x-10$

$3x+7$

$-3x+7$

$3x-7$ ✓

$-3x-7$
Expand $-f(3e+2f-g)$

$-3e^2f-2f^2+fg$

$-3ef-f^2+fg$

$-3ef-2f^2-fg$

$-3ef-2f^2+fg$ ✓

In algebra, when we write the expression $6(y-7)$ as $6y-42$ it is called __________.

factorising

expanding ✓

simplifying ✓

dividing
Expand $-2x(5-x)$

$-10x+2x^2$ ✓

$3x-x$

$-10x-2x^2$

$10x+2x^2$
Expand and simplify $2(y+3)+7(y-1)$

$2y+6-7y-7 \equiv -y-1$

$2y+6+7y-7 \equiv 9y-1$ ✓

$2y+6+7y-7 \equiv 9y+1$

$2y+3+7y-1 \equiv 9y+2$
Match the expressions.

$5(x+4)+3(x+8)$

⇔

$8x+44$ ✓

$5(x+4)+8(x+3)$

⇔

$13x+44$ ✓

$4(x+5)+3(x+8)$

⇔

$7x+44$ ✓

$4(x+5)+8(x-3)$

⇔

$12x-4$ ✓

$4(x-5)+8(x+3)$

⇔

$12x+4$ ✓
Expand and simplify $2d(d-3)-5(d+e)$

$2d^2+11d-5e$

$2d^2-8d-5e$

$2d^2-11d+5e$

$2d^2-11d-5e$ ✓
Match the expressions.

$x(x+y-7)-3x(x-2y)$

⇔

$-2x^2-7x+7xy$ ✓

$x(x+y-7)+3x(x-2y)$

⇔

$4x^2-7x-5xy$ ✓

$-x(x+y-7)+3x(x-2y)$

⇔

$2x^2+7x-7xy$ ✓

$-x(x+y-7)-3x(x-2y)$

⇔

$-4x^2+7x+5xy$ ✓

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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.

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.