- Year 9
More complex binomial products
I can find more complex binomial products.
Lesson details
Key learning points
- The coefficients of the variable(s) may not be one.
- Sometimes the terms within each binomial are not in the same order.
- Multiplication and addition/subtraction with negative numbers is useful here.
Keywords
Binomial - A binomial is an algebraic expression representing the sum of exactly 2 unlike terms.
Common misconception
Mistakes with partial products are even more common where algebraic terms in the binomials have coefficients greater than 1. It is common to find pupils writing that the product of 2x and 3x is 5x
Reminding pupils that because multiplication is commutative the product of 2x and 3x can be thought of as 2 × 3 × x × x
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which of these expressions are binomials?
Q2.Which of these are equivalent to $$a - 6$$ ?
Q3.In the expression $$6x + 4$$, you call 6 the of $$x$$.
Q4.Match each product to its simplified form.
$$x \times -x$$ -Â $$-x^2$$
$$-x\times -x$$ -Â $$x^2$$
$$-2x \times -3x$$ -Â $$6x^2$$
$$-6x \times y$$ -Â $$-6xy$$
$$-3y \times -2x$$ -Â $$6xy$$
$$6x\times -x$$ -Â $$-6x^2$$
Q5.Which of these expressions can be written as the difference of two squares?
Q6.Match each product of two binomials to its expanded form.
$$(x - 5)^2$$ -Â $$x^2 - 10x + 25$$
$$(x - 4)(x - 6)$$ -Â $$x^2 - 10x + 24$$
$$(x + 2)(x - 12)$$ -Â $$x^2 - 10x - 24$$
$$(x + 4)(x - 6)$$ -Â $$x^2 - 2x - 24$$
$$(x + 4)(x + 6)$$ -Â $$x^2 + 10x + 24$$
$$(x + 12)(x - 2)$$ -Â $$x^2 + 10x - 24$$
Assessment exit quiz
6 Questions
Q1.Which binomial expression is equivalent to $$8 - x$$ ?
Q2.Which product of two binomials is equivalent to $$(x - 5)(5 - x)$$ ?
Q3.Which of these expressions can be written as the difference of two squares?
Q4.Match each product of two binomials to its expanded form.
$$(x + 4)(4 -x)$$ -Â $$-x^2 +16$$
$$(x - 4)(4 -x)$$ -Â $$-x^2 +8x -16$$
$$(x - 4)(4 + x)$$ -Â $$x^2 -16$$
$$(x - 4)(-4 +x)$$ -Â $$x^2 - 8x + 16$$
Q5.$$(3x -1)(2x + 5)$$ can be expanded and simplified to give $$6x^2 +$$ $$x - 5$$.
Q6.Expand and simplify $$(2b - 3a)(2a - 3b)$$.
