You can use the rule for the p ro d u c t of a sum a n d difference to calculate pro d u cts using
m en tal m ath.How can you w rite
64 • 56 as the
product of a sum and
difference?
Find th e n u m b e r h a lfw a y
between the factors.
6 0 is 4 u nits fro m each
factor. W rite the factors
in term s o f 60 and 4.
Using M ent al M at h
What is 64 • 56?
64 • 56 = (60 + 4)(60 — 4) Write as a product of a sum and a difference.
= 602 - 42 Use (a + b)(a - b) = a2 - b2.
= 3600 - 16 Simplify powers.
= 3584 Simplify.Go t It? 5. W hat is 52 • 48? Use m ental m ath.©RIDDED RESPONSE
3 5 8 4Lesso n Ch eck
Do y o u k n o w H OW?
Simplify each product.Do y o u UN DERSTAN D?
MATHEMAIICAL
PRACTICES- (c + 3)(c + 3) 5. (3x - l)2
- (g -4 )2 6. (4x - 9)(4x + 9)
- (2r — 3)(2r + 3) 7. (7x + 2)(7x + 2)
- A square has side length (2x + 3) in. W hat is th e area
of the square?
8. R e a s o n i n g How do you know w h e th e r it is
convenient to u se th e rule for th e p ro d u ct of a sum
an d difference to m entally m ultiply two num bers?Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
© Practice Simplify each expression.
- (w + 5)2 10. (h + 2)2
- ( a - 8 ) 2 14. (A: - l l ) 2
MATHEMAtlCAL
PRACTICES- (3s+9)2
- (5m -2)2
Geometry The figures below are squares. Find an expression for the area of
each shaded region. Write your answers in standard form.
x + 4 18. x + 3x + 3See Problem 1.- [2n + 7)2
- (4x — 6)2
See Problem 2.